A002637 - OEIS

%I M0050 N0016 #18 Oct 19 2015 17:43:35

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

%D D. H. Lehmer, Review of Loria article, Math. Comp. 2 (1947), 301-302.

%D G. 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 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Wouter Meeussen, <a href="/A002637/b002637.txt">Table of n, a(n) for n = 1..512</a>

%H Gino Loria, <a href="/A002635/a002635.pdf"> Sulla scomposizione di un intero nella somma di numeri poligonali. (Italian).</a> 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 Eric Weisstein, MathWorld, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>

%t 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 ;it/.l[_]->1 - _Wouter Meeussen_, May 17 2008

%K nonn,easy

%O 1,5

%A _N. J. A. Sloane_.

%E More terms from _Naohiro Nomoto_, Feb 28 2002