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A159355 Number of n X n arrays of squares of integers summing to 4. 1
5, 135, 1836, 12675, 58941, 211925, 635440, 1663821, 3921325, 8495531, 17179020, 32795295, 59626581, 103962825, 174792896, 284660665, 450710325, 695946991, 1050740300, 1554600411, 2258257485, 3226077405, 4538848176, 6296973125 (list; graph; refs; listen; history; text; internal format)
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. [From 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(seq(binomial(n^2, 4)+n^2, n=1..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.

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

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Last modified January 24 07:13 EST 2020. Contains 331189 sequences. (Running on oeis4.)