cp's OEIS Frontend

A002637 Number of partitions of n into not more than 5 pentagonal numbers.

%I A002637 M0050 N0016 #30 Feb 16 2025 08:32:26
%S A002637 1,1,1,1,2,1,1,1,1,1,1,2,2,1,2,2,2,1,1,2,1,2,2,3,3,2,3,2,2,2,1,2,1,3,
%T A002637 3,3,4,3,3,2,3,3,1,2,3,4,4,3,4,3,4,3,3,3,3,3,4,5,5,3,3,4,4,3,2,4,3,4,
%U A002637 4,5,6,5,5,4,5,6,3,4,4,6,5,4,5,4,6,4,5,6,4,3,3,8,7,5,6,5,7,5,6,5,3,6,5,7,7
%N A002637 Number of partitions of n into not more than 5 pentagonal numbers.
%D A002637 Gino Loria, Sulla scomposizione di un intero nella somma di numeri poligonali. (Italian) Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 1, (1946). 7-15.
%D A002637 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002637 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002637 Wouter Meeussen, <a href="/A002637/b002637.txt">Table of n, a(n) for n = 1..512</a>
%H A002637 D. H. Lehmer, <a href="https://doi.org/10.1090/S0025-5718-47-99581-1">Recent Mathematical Tables (about Loria article)</a>, Math. Comp. 2 (1947), 301-302.
%H A002637 Gino Loria, <a href="/A002635/a002635.pdf">Sulla scomposizione di un intero nella somma di numeri poligonali</a>, (Italian), Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 1, (1946). 7-15. Also D. H. Lehmer, Review of Loria article, Math. Comp. 2 (1947), 301-302. [Annotated scanned copies]
%H A002637 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>.
%t A002637 it=Expand[Normal @ Series[CoefficientList[Series[Product[(1+(q l[3k^2/2-k/2] x^(3k^2/2-k/2)))^5,{k,512}],{x,0,512}],x],{q,0,5}]]/. (_Integer) q^(e_:1)->1 /.q->1 ; Drop[it/.l[_]->1,1] (* _Wouter Meeussen_, May 17 2008 *)
%K A002637 nonn,easy
%O A002637 1,5
%A A002637 _N. J. A. Sloane_
%E A002637 More terms from _Naohiro Nomoto_, Feb 28 2002