OFFSET
0,3
COMMENTS
For n > 0, a(n) is the n-th row sum of the triangle A325655.
LINKS
Stefano Spezia, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).
FORMULA
O.g.f.: -x*(1 + 5*x + 13*x*2 + 9*x^3 + 4*x^4)/((-1 + x)^5*(1 + x)^2).
E.g.f.: (1/24)*exp(-x)*x*(3 + 21*exp(2*x) + 78*exp(2*x)*x + 54*exp(2*x)*x^2 + 8*exp(2*x)*x*3).
a(n) = a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7) for n > 6.
a(n) = (1/12)*n^2*(4*n^2 + 3*n + 2) if n is even.
a(n) = (1/12)*n*(n + 1)*(4*n^2 - n + 3) if n is odd.
a(n) = n*A173722(2*n). - Stefano Spezia, Dec 21 2021
MAPLE
a:=n->(1/24)*n*(3 - 3*(- 1)^n + 4*n + 6*n^2 + 8*n^3): seq(a(n), n=0..50);
MATHEMATICA
a[n_]:=(1/24)*n*(3 - 3*(- 1)^n + 4*n + 6*n^2 + 8*n^3); Array[a, 50, 0]
PROG
(GAP) Flat(List([0..50], n->(1/24)*n*(3 - 3*(- 1)^n + 4*n + 6*n^2 + 8*n^3)));
(Magma) [(1/24)*n*(3 - 3*(- 1)^n + 4*n + 6*n^2 + 8*n^3): n in [0..50]];
(PARI) a(n) = (1/24)*n*(3 - 3*(- 1)^n + 4*n + 6*n^2 + 8*n^3);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stefano Spezia, May 13 2019
STATUS
approved