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A157052 Number of integer sequences of length n+1 with sum zero and sum of absolute values 6. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
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
MATHEMATICA
Table[n(n+1)(n^4 +2n^3 +11n^2 +10n +12)/36, {n, 50}] (* Wesley Ivan Hurt, Feb 03 2014 *)
PROG
(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
CROSSREFS
Sequence in context: A201236 A206623 A036800 * A280157 A224616 A052633
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Feb 22 2009
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)