Seven Cornered Pascalloid

Here is another Pascalloid, this one based on seven corners. All of the variables for the terms have been given as 1, allowing the terms to collapse to unity. Please bear with, it is big no matter what monitor size. As a Heptagon with no center point, it may relate somehow to the seven variable Hexagonal Pascalloid Type B, but this "Heptalinear" attempt if made will likely have a-linear results, because this is only example minimal comfortable resolution for a polygon of seven corners (@ Specific Resolution (20)X(19), each of seven variables set to 1; terms thus collapsible)

There is a divergence of polynomial accuracy with respect to the seven variable algabreic expansion beginning at N=5. There we find 142 instances of the number 60, whereas in the expansion of (a+b+c+d+e+f+g) N there are only 140 terms with that coefficient. In this Pascalloid at N=5, there are 101 instances of the number 60, whereas in the expansion there are 105. Though this seems to be an error, it is accurate based on the original algorithm, and because our original heptagonal algorithm takes place on a twenty by nineteen cell grid, it is not a precise heptagonal algorithm. The imprecision pointed out here results in those slight "polynomial overlap" errors starting in the following Pascalloid at N=5.

1

total = 70 = 1


1 1
1
1
1
1
1

total = 71 = 7

1 2 1
2 2
2 2
1
2
2 2 1
2 2
2 2
2
2 2
2
2
2
1
2
1
2
2
1

total = 72 = 49

1 3 3 1
3 6 3
3 6 3
3 3
6 6
3 6 3 3 3
3 6 3
1 3 6 3
3
6 6 3
6 6 6 6 1
6 6
6 6
6 6
3
3 6
3 3 6 3
6 6 3
3 3 3
6
6 6 3
6 6
3
6 3
3 3 3 6
3
6
6 6
6
1 3
3 3
3
1
3
6
3
3
3
1

total = 73 = 343

1 4 6 4 1
4 12 12 4
4 12 12 4
6 12 6
12 24 12
4 12 12 4 6 12 6
4 12 12 4
4 4 4 12 12 4
12 12
12 24 12 12 12
12 12 24 24 12 12 4 4
12 24 12
1 12 24 12
4 12 24 12
12 12 6
12 24 12 24 4
6 12 6 24 12 24 12 1
12 24 12 12 12
12 12 6 12 6
24 24
4 12 24 12 12 12
4 12 12 24 12
12 12 12 12
24 12 24 12 12 4
4 6 12 12 24 6 12 24 4
12 12 12
24 24 12
24 24 24 24 4
6 24 24
12 12
4 4 12 12 6 24 6
12 12 12 12 12 12
12 12 12 6
12 24 4 4
12 12 24 12
24 24 12
4 6 12 12
12 4 12
12 12 12 12 6
12 12 4 12
12 4
24 12
4 4 12 24
12
1 12
4 12 12
6 12
4
4 4 1
12 4
12
4
6
12
6
4
4
1

total = 74 = 2401


1 5 10 10 5 1
5 20 30 20 5
5 20 30 20 5
10 30 30 10
20 60 60 20
5 20 30 20 10 5 30 30 10
5 20 30 20 5
10 20 10 5 20 30 20 5
30 60 30
20 60 60 20 30 60 30
20 20 60 60 60 60 20 20 10 20 10
20 60 60 20
5 5 20 60 60 20
20 20 20 60 60 20
30 60 30 30 30
30 60 60 120 30 60 20 20
10 30 30 10 60 30 120 60 60 30 5 5
20 60 60 20 30 60 30
1 30 60 30 10 30 30 10
5 60 120 60
20 20 20 60 10 60 20 30 60 30
20 60 20 60 20 60 10 60 20
30 60 30 60 60 60 60 5
60 30 120 60 60 30 60 20 60 20 1
20 20 10 30 30 60 30 60 120 10 30 60 20 20
60 60 30 60 30
5 60 120 60 60 60
5 20 60 60 120 120 60 60 20 20
30 30 20 30 60 120 60
60 60 60 60 30 20
5 10 20 30 10 60 30 120 30 60 120 30 20 5
20 30 60 60 60 60 60 30 60 60 5
60 60 30 30 60 30 30 30
60 120 60 120 10 20 20 10
10 30 60 30 120 60 120 60 5
20 30 60 120 60 60 60
20 20 30 30 10 60 30 30 60 30
60 20 60 20 60 60 30 60 10
20 30 60 60 60 30 60 60 30 30 30 20
20 60 30 60 20 60 30 20 60 10
60 60 60 60 20 20
120 60 120 60 60 20
10 10 10 20 60 120 10 60 120 20
30 20 30 60 60
5 5 60 60 30 60 10 30
20 20 60 60 60 10 60 60 30 10
30 30 30 60 60 20 30
60 60 20 20 10
20 20 20 20 30 120 30 5 5
60 60 20 20 60 60
5 30 60 60 30
20 5 30 60 20 20
30 30 30 20 60 30
60 60 20 30 30
20 10 30 30 5 20
60 20 20 5
20 20 60 60 10
20 20 20 60
1 30 20
5 60 30
10 5 5 30 60
10 30
5 20 5
20 20 20 1
30 20
20
10 5 5
30 5
30
10
10
20
10
5
5
1

total = 75 = 16,807

1 6 15 20 15 6 1
6 30 60 60 30 6
6 30 60 60 30 6
15 60 90 60 15
30 120 180 120 30
6 30 60 60 15 30 60 6 90 60 15
6 30 60 60 30 6
20 60 60 6 20 30 60 60 30 6
60 180 180 60
30 120 180 120 60 30 180 180 60
30 30 120 120 180 180 120 120 30 20 30 60 60 20
30 120 180 120 30
15 30 15 30 120 180 120 30
60 120 60 30 120 180 120 30
60 180 180 60 90 180 90
60 120 180 360 180 360 60 120 60 120 60
15 60 90 60 120 60 15 360 180 360 180 120 60 15 30 15
30 120 180 120 60 30 180 180 60
6 6 60 180 180 60 15 60 90 60 15