A159375 Number of n X n arrays of squares of integers summing to 9.

16, 766, 61184, 3112500, 105851488, 2138413851, 27990555776, 262835331687, 1909384608000, 11319915386120, 56916060868096, 249702337698346, 976762617522160, 3464394870851125, 11290721919375872, 34177386571594701

Offset

2,1

Comments

All such sequences have holonomic recurrences (cf. comment in A159359). - Georg Fischer, Feb 17 2022

Links

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

Index entries for linear recurrences with constant coefficients, signature (19, -171, 969, -3876, 11628, -27132, 50388, -75582, 92378, -92378, 75582, -50388, 27132, -11628, 3876, -969, 171, -19, 1).

Formula

Empirical g.f.: -x-(1+x)*x*(1 - 4*x + 637*x^2 + 47760*x^3 + 2021602*x^4 + 54462984*x^5 + 548532899*x^6 + 2125377516*x^7 + 3360726010*x^8 + 2125377516*x^9 + 548532899*x^10 + 54462984*x^11 + 2021602*x^12 + 47760*x^13 + 637*x^14 - 4*x^15 + x^16)/(-1+x)^19. - Vaclav Kotesovec, Nov 30 2012

a(n) = binomial(n^2,1) + multinomial(n^2,1,2,(n^2-3)) + multinomial(n^2,1,5,n^2-6) + binomial(n^2,9) = (1/362880)*n^18 - (1/10080)*n^16 + (13/8640)*n^14 - (1/240)*n^12 - (1091/17280)*n^10 + (251/480)*n^8 - (95209/90720)*n^6 + (1213/2520)*n^4 + (10/9)*n^2 corresponding to the ways of obtaining 9 as a sum of n^2 squares: 9 + (n^2-1)*0, 2*4 + 1 + (n^2-3)*0, 4 + 5*1 + (n^2 - 6)*0, and 9*1 + (n^2 - 9)*0. - Robert Israel, Dec 18 2023

Crossrefs

Sequence in context: A218297 A339202 A307923 * A221527 A129008 A134183

Adjacent sequences: A159372 A159373 A159374 * A159376 A159377 A159378

Keyword

nonn

Author

R. H. Hardin, Apr 11 2009

Status

approved