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A157534
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Half the number of length n integer sequences with sum zero and sum of squares 8.
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1
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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
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OFFSET
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2,2
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LINKS
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FORMULA
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[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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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