A157052 Number of integer sequences of length n+1 with sum zero and sum of absolute values 6.
2, 18, 92, 340, 1010, 2562, 5768, 11832, 22530, 40370, 68772, 112268, 176722, 269570, 400080, 579632, 822018, 1143762, 1564460, 2107140, 2798642, 3670018, 4756952, 6100200, 7746050, 9746802, 12161268, 15055292, 18502290, 22583810, 27390112, 33020768, 39585282
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Maple
A157052:=n->n*(n + 1)*(n^4 + 2*n^3 + 11*n^2 + 10*n + 12)/36; seq(A157052(n), n=1..50); # Wesley Ivan Hurt, Feb 03 2014
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Mathematica
Table[n(n+1)(n^4 +2n^3 +11n^2 +10n +12)/36, {n, 50}] (* Wesley Ivan Hurt, Feb 03 2014 *) -
Sage
[n*(n+1)*(n^4 +2*n^3 +11*n^2 +10*n +12)/36 for n in (1..50)] # G. C. Greubel, Jan 23 2022
Formula
a(n) = T(n,3); T(n,k) = Sum_{i=1..n} binomial(n+1,i)*binomial(k-1,i-1)*binomial(n-i+k,k).
G.f.: 2*x*(1+2*x+4*x^2+2*x^3+x^4)/(1-x)^7. - Colin Barker, Mar 17 2012
a(n) = n*(n+1)*(n^4 +2*n^3 +11*n^2 +10*n +12)/36. - Bruno Berselli, Mar 17 2012
E.g.f.: (x/36)*(72 + 252*x + 264*x^2 + 108*x^3 + 18*x^4 + x^5)*exp(x). - G. C. Greubel, Jan 23 2022