A288253 - OEIS

%I #33 Mar 10 2023 03:17:42

%S 1,1,2,3,5,6,10,13,19,24,34,42,58,70,93,112,145,171,218,256,320,372,

%T 458,528,643,735,884,1006,1198,1352,1597,1795,2102,2350,2732,3041,

%U 3513,3892,4468,4934,5633,6194,7037,7715,8722,9531,10728,11690

%N Number of heptagons that can be formed with perimeter n.

%C Number of (a1, a2, ... , a7) where 1 <= a1 <= ... <= a7 and a1 + a2 + ... + a6 > a7.

%H Seiichi Manyama, <a href="/A288253/b288253.txt">Table of n, a(n) for n = 7..10000</a>

%H G. E. Andrews, P. Paule and A. Riese, <a href="http://www.risc.jku.at/publications/download/risc_163/PAIX.pdf">MacMahon's Partition Analysis IX: k-gon partitions</a>, Bull. Austral Math. Soc., 64 (2001), 321-329.

%H Geoffrey Critzer, <a href="https://esirc.emporia.edu/handle/123456789/3595">Combinatorics of Vector Spaces over Finite Fields</a>, Master's thesis, Emporia State University, 2018. [This thesis cites this sequence entry, but it's just a typo: the intended sequence entry is A288853.]

%H <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, 1, 0, 0, 1, 0, -1, -1, -1, 0, 0, -2, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, -1, 0, -1, -2, -1, 0, -1, -1, 0, 0, 2, 0, 0, 1, 1, 1, 0, -1, 0, 0, -1, 0, -1, 0, 1).

%F G.f.: x^7/((1-x)*(1-x^2)* ... *(1-x^7)) - x^12/(1-x) * 1/((1-x^2)*(1-x^4)* ... *(1-x^12)).

%F a(2*n+12) = A026813(2*n+12) - A288341(n), a(2*n+13) = A026813(2*n+13) - A288341(n) for n >= 0. - _Seiichi Manyama_, Jun 08 2017

%Y Number of k-gons that can be formed with perimeter n: A005044 (k=3), A062890 (k=4), A069906 (k=5), A069907 (k=6), this sequence (k=7), A288254 (k=8), A288255 (k=9), A288256 (k=10).

%K nonn,easy

%O 7,3

%A _Seiichi Manyama_, Jun 07 2017