login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A288256
Number of decagons that can be formed with perimeter n.
11
1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 71, 93, 121, 157, 200, 255, 321, 404, 500, 623, 762, 939, 1137, 1388, 1664, 2015, 2396, 2877, 3398, 4050, 4748, 5623, 6553, 7711, 8936, 10454, 12051, 14024, 16088, 18626, 21275, 24516, 27882, 31991, 36244, 41411, 46746
OFFSET
10,3
COMMENTS
Number of (a1, a2, ... , a10) where 1 <= a1 <= ... <= a10 and a1 + a2 + ... + a9 > a10.
LINKS
G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis IX: k-gon partitions, Bull. Austral Math. Soc., 64 (2001), 321-329.
Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 1, 1, 0, -1, 0, -1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 2, 1, 1, 0, 1, -2, 1, -1, 0, -1, -1, -1, -1, 0, -1, 1, -2, 1, -1, 1, -1, 2, 1, 1, 1, 1, 2, -1, 1, -1, 1, -2, 1, -1, 0, -1, -1, -1, -1, 0, -1, 1, -2, 1, 0, 1, 1, 2, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, -1, -1, 0, -1, 0, 1, 1, 0, 1, 0, -1).
FORMULA
G.f.: x^10/((1-x)*(1-x^2)* ... *(1-x^10)) - x^18/(1-x) * 1/((1-x^2)*(1-x^4)* ... *(1-x^18)).
a(2*n+18) = A026816(2*n+18) - A288344(n), a(2*n+19) = A026816(2*n+19) - A288344(n) for n >= 0.
CROSSREFS
Number of k-gons that can be formed with perimeter n: A005044 (k=3), A062890 (k=4), A069906 (k=5), A069907 (k=6), A288253 (k=7), A288254 (k=8), A288255 (k=9), this sequence (k=10).
Sequence in context: A232480 A332638 A035977 * A101049 A333193 A035986
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 07 2017
STATUS
approved