A159355 Number of n X n arrays of squares of integers summing to 4.

5, 135, 1836, 12675, 58941, 211925, 635440, 1663821, 3921325, 8495531, 17179020, 32795295, 59626581, 103962825, 174792896, 284660665, 450710325, 695946991, 1050740300, 1554600411, 2258257485, 3226077405, 4538848176, 6296973125, 8624108701, 11671286355

Offset

2,1

Comments

Each array either has four 1's or one 4, and all other elements 0. - Robert Israel, Jun 19 2018

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

Empirical: n^2*(n^2+1)*(n^4-7*n^2+18)/24. - R. J. Mathar, Aug 11 2009

From Robert Israel, Jun 19 2018: (Start)

Empirical formula confirmed.

a(n) = binomial(n^2,4)+n^2 = A014626(n^2).

(End)

From Colin Barker, Jun 19 2018: (Start)

G.f.: x^2*(5 + 90*x + 801*x^2 + 591*x^3 + 252*x^4 - 88*x^5 + 37*x^6 - 9*x^7 + x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>10.

(End)

Maple

seq(binomial(n^2, 4)+n^2, n=2..100);

Prog

(PARI) Vec(x^2*(5 + 90*x + 801*x^2 + 591*x^3 + 252*x^4 - 88*x^5 + 37*x^6 - 9*x^7 + x^8) / (1 - x)^9 + O(x^40)) \\ Colin Barker, Jun 19 2018

Crossrefs

Cf. A014626, A159359.

Sequence in context: A307084 A132508 A215218 * A184577 A229772 A082212

Adjacent sequences: A159352 A159353 A159354 * A159356 A159357 A159358

Keyword

nonn,easy

Author

R. H. Hardin, Apr 11 2009

Status

approved