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

2,1

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

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

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 *)

Crossrefs

Cf. A159355-A159446.

Sequence in context: A185247 A368771 A009530 * A009680 A218820 A231520

Adjacent sequences: A159360 A159361 A159362 * A159364 A159365 A159366

Keyword

nonn,easy

Author

R. H. Hardin, Apr 11 2009

Status

approved