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

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, 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, 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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• 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.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Wouter Meeussen, Table of n, a(n) for n = 1..512
• D. H. Lehmer, Recent Mathematical Tables (about Loria article), Math. Comp. 2 (1947), 301-302.
• 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. Also D. H. Lehmer, Review of Loria article, Math. Comp. 2 (1947), 301-302. [Annotated scanned copies]
• Eric Weisstein's World of Mathematics, Pentagonal Number.

Programs

Mathematica

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 *)

Extensions

More terms from Naohiro Nomoto, Feb 28 2002