A157534 Half the number of length n integer sequences with sum zero and sum of squares 8.

1, 3, 6, 30, 135, 441, 1183, 2871, 6660, 15070, 33231, 70863, 145236, 285390, 537930, 974746, 1703043, 2878101, 4719220, 7529340, 11718861, 17834223, 26591841, 38918025, 55995550, 79317576, 110749653, 152600581, 207702930, 279504060

Offset

2,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

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,0,8)/2.

G.f.: x^2*(1-6*x+15*x^2-45*x^4+54*x^5+16*x^6)/(1-x)^9. - Colin Barker, Feb 22 2012

a(n) = n (n-1)(n^6-27 n^5+295 n^4-1473 n^3+3376 n^2-3036 n+1008)/1152. - Robert Israel, Apr 07 2014

Crossrefs

Sequence in context: A280981 A265376 A318431 * A372024 A133799 A347925

Adjacent sequences: A157531 A157532 A157533 * A157535 A157536 A157537

Keyword

nonn,easy

Author

R. H. Hardin, Mar 02 2009

Status

approved