OFFSET
0,2
COMMENTS
Row sums of A124819.
Let M = a triangle with the triangular series in every column, but the leftmost column is shifted upwards one row. Then A124820 = Lim_{n->inf} M^n, the left-shifted vector considered as a sequence. - Gary W. Adamson, Jul 27 2010
Second trisection of Narayana's cows sequence A000930. - Oboifeng Dira, Aug 03 2016
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-3,1).
FORMULA
a(n) = sum( k=0..n, C(n+2k+1, 3k+1) ).
MATHEMATICA
CoefficientList[Series[(1 - x)/(1 - 4 x + 3 x^2 - x^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jun 20 2014 *)
LinearRecurrence[{4, -3, 1}, {1, 3, 9}, 30] (* Harvey P. Dale, Apr 29 2016 *)
Table[Sum[Binomial[n + 2 k + 1, 3 k + 1], {k, 0, n}], {n, 0, 25}] (* Michael De Vlieger, Aug 03 2016 *)
PROG
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, -3, 4]^n*[1; 3; 9])[1, 1] \\ Charles R Greathouse IV, Aug 03 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Nov 08 2006
STATUS
approved