A157052 - OEIS

%I #19 Jan 24 2022 07:04:52

%S 2,18,92,340,1010,2562,5768,11832,22530,40370,68772,112268,176722,

%T 269570,400080,579632,822018,1143762,1564460,2107140,2798642,3670018,

%U 4756952,6100200,7746050,9746802,12161268,15055292,18502290,22583810,27390112,33020768,39585282

%N Number of integer sequences of length n+1 with sum zero and sum of absolute values 6.

%H T. D. Noe, <a href="/A157052/b157052.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F 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).

%F G.f.: 2*x*(1+2*x+4*x^2+2*x^3+x^4)/(1-x)^7. - _Colin Barker_, Mar 17 2012

%F a(n) = n*(n+1)*(n^4 +2*n^3 +11*n^2 +10*n +12)/36. - _Bruno Berselli_, Mar 17 2012

%F 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

%p 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

%t Table[n(n+1)(n^4 +2n^3 +11n^2 +10n +12)/36, {n, 50}] (* _Wesley Ivan Hurt_, Feb 03 2014 *)

%o (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

%Y Cf. A103881, A156554.

%K nonn,easy

%O 1,1

%A _R. H. Hardin_, Feb 22 2009