|
| |
|
|
A037444
|
|
Number of partitions of n^2 into squares.
|
|
8
| |
|
|
1, 1, 2, 4, 8, 19, 43, 98, 220, 504, 1116, 2468, 5368, 11592, 24694, 52170, 108963, 225644, 462865, 941528, 1899244, 3801227, 7550473, 14889455, 29159061, 56722410, 109637563, 210605770, 402165159, 763549779, 1441686280, 2707535748, 5058654069, 9404116777
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Is limit_{n->inf} a(n)^(1/n) > 1? - Paul D. Hanna, Aug 20 2002
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..100
|
|
|
FORMULA
| a(n) = A001156(n^2) = coefficient of x^(n^2) in the series expansion of prod(k>=1, 1/(1 - x^(k^2)) ).
|
|
|
MATHEMATICA
| max=33; se = Series[ Product[1/(1-x^(k^2)), {k, 1, max}], {x, 0, max^2}]; a[n_] := Coefficient[se, x^(n^2)]; a[0] = 1; Table[a[n], {n, 0, max}] (* From Jean-François Alcover, Oct 18 2011 *)
|
|
|
PROG
| (Haskell)
a037444 n = p (map (^ 2) [1..]) (n^2) where
p _ 0 = 1
p ks'@(k:ks) m | m < k = 0
| otherwise = p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Aug 14 2011
|
|
|
CROSSREFS
| Entries with square index in A001156.
Cf. A072964.
Cf. A030273, A000041, A000290.
Sequence in context: A018306 A139784 A199694 * A151526 A099526 A005703
Adjacent sequences: A037441 A037442 A037443 * A037445 A037446 A037447
|
|
|
KEYWORD
| nonn,nice,easy
|
|
|
AUTHOR
| W. Meeussen (wouter.meeussen(AT)pandora.be)
|
| |
|
|
