A157535 Half the number of length n integer sequences with sum zero and sum of squares 18.

1, 3, 18, 70, 285, 1533, 7084, 29604, 116385, 419815, 1385142, 4278066, 12678757, 36517950, 102364200, 278451568, 733599079, 1872496417, 4639365470, 11183927650, 26287242751, 60341512253, 135432776524, 297482865100

Offset

2,2

Links

R. H. Hardin, Table of n, a(n) for n=2..50

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,0,18)/2.

G.f.: -x^2*(434*x^16 +19697*x^15 +99303*x^14 -116957*x^13 -153862*x^12 +406284*x^11 -362744*x^10 +160940*x^9 -16710*x^8 -25990*x^7 +20878*x^6 -9354*x^5 +3002*x^4 -728*x^3 +132*x^2 -16*x +1) / (x -1)^19. - Colin Barker, Apr 08 2014

Crossrefs

Sequence in context: A048899 A337142 A107583 * A098522 A174764 A114633

Adjacent sequences: A157532 A157533 A157534 * A157536 A157537 A157538

Keyword

nonn,easy

Author

R. H. Hardin, Mar 02 2009

Status

approved