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A093116 Number of partitions of n^2 into squares not less than n. 5
1, 1, 1, 1, 2, 2, 2, 1, 2, 5, 4, 4, 5, 9, 15, 23, 24, 13, 20, 32, 55, 84, 113, 185, 303, 545, 167, 298, 435, 716, 1055, 1701, 2584, 4213, 6471, 10218, 15884, 4856, 7376, 11231, 17221, 26054, 39583, 60109, 91622, 138569, 209951, 318368, 483098, 730183 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

EXAMPLE

n=10: 10^2 = 100 = 64+36 = 36+16+16+16+16 = 25+25+25+25, all other partitions of 100 into squares contain parts < 10, therefore a(10) = 4.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1,

     `if`(i^2>n, 0, b(n, i+1) +b(n-i^2, i)))

    end:

a:= proc(n) local r; r:= isqrt(n);

      b(n^2, r+`if`(r^2<n, 1, 0))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, Apr 15 2013

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0, 1, If[i^2>n, 0, b[n, i+1] + b[n-i^2, i]]]; a[n_] := With[{r = Sqrt[n]//Floor}, b[n^2, r + If[r^2<n, 1, 0]]]; Table[ a[n], {n, 0, 50}] (* Jean-François Alcover, Oct 26 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A093115, A092362, A001156, A037444, A078134.

Cf. A072213, A161408. [Reinhard Zumkeller, Jun 10 2009]

Sequence in context: A253196 A271205 A303841 * A327799 A198199 A124369

Adjacent sequences:  A093113 A093114 A093115 * A093117 A093118 A093119

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 21 2004

STATUS

approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)