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A190089
Row sums of the triangular matrix A190088.
3
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)
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
Sequence in context: A027909 A127111 A270787 * A349300 A240436 A255139
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, May 04 2011
STATUS
approved