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 A030273 Number of partitions of n^2 into distinct squares. 15
 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 3, 4, 2, 7, 8, 12, 13, 16, 25, 28, 55, 51, 91, 90, 158, 176, 288, 297, 487, 521, 847, 908, 1355, 1580, 2175, 2744, 3636, 4452, 5678, 7385, 9398, 11966, 14508, 19322, 23065, 31301, 36177, 49080, 57348, 77446, 91021, 121113, 141805 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..1000 (terms 0..750 from Alois P. Heinz) FORMULA a(n) = [x^(n^2)] Product_{k>=1} (1 + x^(k^2)). - Ilya Gutkovskiy, Apr 13 2017 MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(n>i*(i+1)*(2*i+1)/6, 0, b(n, i-1)+ `if`(i^2>n, 0, b(n-i^2, i-1)))) end: a:= n-> b(n^2, n): seq(a(n), n=0..50); # Alois P. Heinz, Nov 20 2012 MATHEMATICA b[n_, i_] := b[n, i] = If[n==0, 1, If[n > i*(i+1)*(2*i+1)/6, 0, b[n, i-1] +If[i^2 > n, 0, b[n-i^2, i-1]]]]; a[n_] := b[n^2, n]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 30 2015, after Alois P. Heinz *) PROG (Haskell) a030273 n = p (map (^ 2) [1..]) (n^2) where p _ 0 = 1 p (k:ks) m | m < k = 0 | otherwise = p ks (m - k) + p ks m -- Reinhard Zumkeller, Aug 14 2011 CROSSREFS Cf. A037444, A033461, A000009, A000290. Sequence in context: A275078 A286478 A340756 * A029197 A029174 A058753 Adjacent sequences: A030270 A030271 A030272 * A030274 A030275 A030276 KEYWORD nonn AUTHOR Warren D. Smith EXTENSIONS a(0)=1 prepended by Alois P. Heinz, Feb 18 2015 STATUS approved

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Last modified February 27 14:28 EST 2024. Contains 370376 sequences. (Running on oeis4.)