A159363 Number of n X n arrays of squares of integers summing to 6.

12, 336, 9688, 184000, 1969212, 14039088, 75099360, 324796176, 1192537500, 3844187424, 11144826264, 29583574384, 72891000364, 168494340000, 368541092736, 768025638240, 1533632745708, 2948331631152, 5478589599000, 9873410641248, 17307337994716, 29583198551632

Offset: 2

Author

R. H. Hardin, Apr 11 2009

Keywords

• nonn
• easy

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 (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

Crossrefs

Cf. A159355-A159446.

Programs

Maple

C:=binomial; seq(n^2*C(n^2-1,2)+C(n^2,6),n=2..22); # Georg Fischer, Feb 18 2022

Mathematica

RecurrenceTable[{a[n-1] * (600*n+600*n^2-206*n^3-206*n^4-71*n^5-71*n^6+14*n^7+14*n^8-n^9-n^10) + a[n] * (-672-232*n+2424*n^2-2090*n^3+492*n^4+203*n^5-125*n^6-30*n^7+40*n^8-11*n^9+n^10) == 0, a[2]==12}, a[n], {n,2,20}] (* Georg Fischer, Feb 18 2022 *)

Formula

Empirical g.f.: -4*x^2*(1+x)*(3 + 42*x + 1522*x^2 + 18686*x^3 + 42654*x^4 + 18686*x^5 + 1522*x^6 + 42*x^7 + 3*x^8)/(-1+x)^13. - Vaclav Kotesovec, Nov 30 2012