A157536 Half the number of length n integer sequences with sum zero and sum of squares 32.

1, 3, 6, 110, 1095, 7161, 37919, 182367, 860400, 3893395, 17126571, 73368945, 300879670, 1173812745, 4380376770, 15753693858, 54909242667, 186135465987, 614751720490, 1979351435670, 6214975736739, 19042979887371, 57000797449509

Offset

2,2

Links

Robert Israel and R. H. Hardin, Table of n, a(n) for n = 2..10000 (n = 2..50 from R. H. Hardin)

Formula

[cache enabling] count(n,s,ss)->count(n,t,tt) where t=s mod n, q=(t-s)/n, tt=ss+2*q*s+n*q^2; count(n,t,tt)=Sum_{i^2<=tt} count(n-1,t-i,tt-i^2). a(n)=count(n,0,32)/2.

G.f.: (1 - 30*x + 435*x^2 - 3960*x^3 + 25185*x^4 - 118206*x^5 + 420686*x^6 - 1134432*x^7 + 2206965*x^8 - 2665333*x^9 + 3050124*x^10 - 34121034*x^11 + 301563025*x^12 - 1647844221*x^13 + 6443298873*x^14 - 19087013776*x^15 + 43441736331*x^16 - 74712136848*x^17 + 90999467153*x^18 - 61749383676*x^19 - 17226181401*x^20 + 95716380496*x^21 - 106118533542*x^22 + 46133383200*x^23 + 12059750667*x^24 - 19161162021*x^25 + 2427632556*x^26 + 2280934382*x^27 + 225810123*x^28 + 5162259*x^29 + 16214*x^30) * x^2/(1-x)^33. - Robert Israel, Dec 25 2016

Maple

g:= proc(n, s, ss) option remember;
   if n = 1 then if ss = s^2 then return 1 else return 0 fi fi;
   procname(n-1, s, ss) +  add(procname(n-1, s-t, ss-t^2)
      +procname(n-1, s+t, ss-t^2), t=1..floor(sqrt(ss)));
end proc:
seq(g(n, 0, 32)/2, n=2..50); # Robert Israel, Dec 25 2016

Mathematica

g[n_, s_, ss_] := g[n, s, ss] = If[n == 1, If[ss == s^2, 1, 0], g[n-1, s, ss] + Sum[g[n-1, s-t, ss-t^2] + g[n-1, s+t, ss-t^2], {t, 1, Floor[Sqrt[ss]]}]];
Table[g[n, 0, 32]/2, {n, 2, 50}] (* Jean-François Alcover, Aug 28 2022, after Robert Israel *)

Crossrefs

Sequence in context: A092680 A101574 A082980 * A046488 A074880 A225884

Adjacent sequences: A157533 A157534 A157535 * A157537 A157538 A157539

Keyword

nonn

Author

R. H. Hardin, Mar 02 2009

Status

approved