A159379 Number of n X n arrays of squares of integers summing to 10.

18, 1080, 99248, 6710160, 312975306, 8820400232, 155825544448, 1902742912440, 17422385919290, 126966804496576, 769002076834992, 3997219502682952, 18271131867527266, 74845992604425840, 278918348891883520, 957055146953124368, 3053791953265318722

Offset

2,1

Links

R. H. Hardin, Table of n, a(n) for n=2..100

Index entries for linear recurrences with constant coefficients, signature (21, -210, 1330, -5985, 20349, -54264, 116280, -203490, 293930, -352716, 352716, -293930, 203490, -116280, 54264, -20349, 5985, -1330, 210, -21, 1).

Formula

Empirical G.f.: -2*x^2*(1+x)*(9 + 342*x + 39832*x^2 + 2374574*x^3 + 93413104*x^4 + 1672161938*x^5 + 12313058136*x^6 + 40002238314*x^7 + 59444070702*x^8 + 40002238314*x^9 + 12313058136*x^10 + 1672161938*x^11 + 93413104*x^12 + 2374574*x^13 + 39832*x^14 + 342*x^15 + 9*x^16)/(-1+x)^21. - Vaclav Kotesovec, Nov 30 2012

a(n) = multinomial(n^2,1,1,n-2) + multinomial(n^2,2,2,n^2-4) + multinomial(n^2,1,6,n^2-7) + binomial(n^2,10)

= (n^20 - 45*n^18 + 870*n^16 - 4410*n^14 - 42567*n^12 + 612675*n^10 - 2073520*n^8 + 1569060*n^6 + 5744016*n^4 - 5806080*n^2)/3628800,

corresponding to the ways of obtaining 10 as a sum of n^2 squares:

9 + 1 + (n^2-2)*0, 2*4 + 2*1 + (n^2-4)*0, 4 + 6*1 + (n^2 - 7)*0, and 10*1 + (n^2 - 10)*0. - Robert Israel, Dec 20 2023

Crossrefs

Sequence in context: A214232 A146197 A301651 * A323571 A052135 A033518

Adjacent sequences: A159376 A159377 A159378 * A159380 A159381 A159382

Keyword

nonn,easy

Author

R. H. Hardin, Apr 11 2009

Status

approved