OFFSET
0,4
COMMENTS
Diagonal sums of number triangle A116089.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0, 1, 3, 3, 1).
FORMULA
a(n) = a(n-2) + 3*a(n-3) + 3*a(n-4) + a(n-5).
a(n) = Sum_{k=0..floor(n/2)} C(3*k, n-2*k).
a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*C(4*k,n-k)/C(4*k,k).
MATHEMATICA
CoefficientList[Series[1/(1-x^2(1+x)^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 1, 3, 3, 1}, {1, 0, 1, 3, 4}, 40] (* Harvey P. Dale, Apr 28 2014 *)
PROG
(PARI) {a(n) = sum(k=0, floor(n/2), binomial(3*k, n-2*k))}; \\ G. C. Greubel, May 09 2019
(Magma) [(&+[Binomial(3*k, n-2*k): k in [0..Floor(n/2)]]): n in [0..40]]; // G. C. Greubel, May 09 2019
(Sage) [sum(binomial(3*k, n-2*k) for k in (0..floor(n/2))) for n in (0..40)] # G. C. Greubel, May 09 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 04 2006
STATUS
approved