A190089 Row sums of the triangular matrix A190088.
1, 4, 21, 114, 616, 3329, 17991, 97229, 525456, 2839729, 15346786, 82938844, 448227521, 2422362079, 13091204281, 70748973084, 382349636061, 2066337330754, 11167134898976, 60350698792449, 326154101090951, 1762639037938629, 9525854090667496, 51480702630305689, 278217860370802066
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1350 (terms 0..136 from Vincenzo Librandi)
- Index entries for linear recurrences with constant coefficients, signature (5,2,1).
Programs
-
Magma
[(&+[Binomial(3*n-k+1,3*n-3*k+1): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Mar 04 2018
-
Mathematica
Table[Sum[Binomial[3n - k + 1, 3n - 3k + 1], {k, 0, n}], {n, 0, 12}] LinearRecurrence[{5,2,1},{1,4,21},30] (* Harvey P. Dale, Sep 18 2013 *) -
Maxima
makelist(sum(binomial(3*n-k+1,3*n-3*k+1),k,0,n),n,0,24);
-
PARI
Vec((1-x-x^2)/(1-5*x-2*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Jun 30 2011
Formula
a(n) = Sum_{k=0..n} binomial(3*n-k+1,3*n-3*k+1).
G.f.: (1-x-x^2)/(1-5*x-2*x^2-x^3).
a(n) = 5*a(n-1)+2*a(n-2)+a(n-3) and a(0)=1, a(1)=4, a(2)=21. - Harvey P. Dale, Sep 18 2013