A331907 Triangle read by rows: Take a pentagram with all diagonals drawn, as in A331906. Then T(n,k) = number of k-sided polygons in that figure for k = 3, 4, ..., n+2.

40, 0, 0, 590, 420, 80, 10, 2890, 3030, 1130, 230, 50, 9540, 10530, 4290, 980, 190, 10, 22730, 28390, 10960, 3200, 550, 80, 20, 47610, 57450, 23270, 6530, 1160, 160, 20, 0, 90080, 109160, 47430, 13430, 2460, 410, 40, 0, 0, 154840, 193480, 82330, 22410, 4620

Offset

1,1

Comments

See the links in A331906 for images of the pentagrams.

Links

Lars Blomberg, Table of n, a(n) for n = 1..250 (the first 20 rows)

Eric Weisstein's World of Mathematics, Pentagram.

Example

A pentagram with no other points along its edges, n = 1, contains 40 triangles and no other n-gons, so the first row is [40,0,0]. A pentagram with 1 point dividing its edges, n = 2, contains 590 triangles, 420 quadrilaterals, 80 pentagons and 10 hexagons, so the second row is [590,420,80,10].
Triangle begins:
40,0,0
590, 420, 80, 10
2890, 3030, 1130, 230, 50
9540, 10530, 4290, 980, 190, 10
22730, 28390, 10960, 3200, 550, 80, 20
47610, 57450, 23270, 6530, 1160, 160, 20, 0
The row sums are A331906.

Crossrefs

Cf. A331906 (regions), A333117 (vertices), A333118 (edges), A007678, A092867, A331452.

Sequence in context: A023931 A067159 A292152 * A247404 A013373 A013375

Adjacent sequences: A331904 A331905 A331906 * A331908 A331909 A331910

Keyword

nonn,tabf

Author

Scott R. Shannon and N. J. A. Sloane, Jan 31 2020

Extensions

a(34) and beyond from Lars Blomberg, May 06 2020

Status

approved