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A159363 Number of n X n arrays of squares of integers summing to 6. 1
12, 336, 9688, 184000, 1969212, 14039088, 75099360, 324796176, 1192537500, 3844187424, 11144826264, 29583574384, 72891000364, 168494340000, 368541092736, 768025638240, 1533632745708, 2948331631152, 5478589599000, 9873410641248, 17307337994716, 29583198551632 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
All such sequences have holonomic recurrences (cf. comment in A159359). - Georg Fischer, Feb 17 2022
LINKS
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
Sequence in context: A185247 A368771 A009530 * A009680 A218820 A231520
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Apr 11 2009
STATUS
approved

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Last modified May 26 23:01 EDT 2024. Contains 372847 sequences. (Running on oeis4.)