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A355839
Number of vertices formed in a square by straight line segments when connecting the n+1 points along each edge that divide it into n equal parts to the n+1 points on the edge on the opposite side of the square.
6
5, 25, 133, 357, 1013, 1637, 3761, 5561, 9313, 13065, 21689, 25357, 41553, 50157, 66005, 84897, 117793, 129841, 181717, 198857, 251189, 302293, 383161, 401073, 517193, 587041, 687765, 763425, 949869, 966249, 1234425, 1320913, 1512233, 1703657, 1912765, 2023569, 2475361, 2649813, 2934997
OFFSET
1,1
COMMENTS
This sequence is similar to A355799 but here the corner vertices of the square are also connected to points on the opposite edge.
LINKS
Scott R. Shannon, Image for n = 2.
Scott R. Shannon, Image for n = 3.
Scott R. Shannon, Image for n = 4.
Scott R. Shannon, Image for n = 5.
Scott R. Shannon, Image for n = 6.
Scott R. Shannon, Image for n = 11.
FORMULA
a(n) = A355840(n) - A355838(n) + 1 by Euler's formula.
CROSSREFS
Cf. A355838 (regions), A355840 (edges), A355841 (k-gons), A355799 (without corner vertices), A290131, A331452, A335678.
Sequence in context: A094602 A207834 A351187 * A344396 A351587 A225963
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Jul 18 2022
STATUS
approved