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

0,2

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).

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A190088, A190090.

Sequence in context: A027909 A127111 A270787 * A349300 A240436 A255139

Adjacent sequences: A190086 A190087 A190088 * A190090 A190091 A190092

Keyword

nonn,easy

Author

Emanuele Munarini, May 04 2011

Status

approved