A358092 Row sums of the convolution triangle of the Motzkin numbers (A202710).

1, 1, 3, 9, 28, 88, 279, 889, 2843, 9115, 29279, 94183, 303294, 977522, 3152709, 10173671, 32844544, 106073200, 342671109, 1107278239, 3578704532, 11568322736, 37400611581, 120931966547, 391065616195, 1264729338163, 4090528413309, 13230930776769, 42798305388298

Offset

0,3

Links

Table of n, a(n) for n=0..28.

Formula

a(n) = [x^n] (sqrt(x + 1)*(1 - 2*x) + sqrt(1 - 3*x)) / (sqrt(x + 1)*(1 - 4*x) + sqrt(1 - 3*x)).

a(n) = ((36-12*n)*a(n-4) + (30-14*n)*a(n-3) + (3*n-3)*a(n-2) + (4*n-3)*a(n-1))/n for n >= 5.

Maple

ogf := (sqrt(x + 1)*(1 - 2*x) + sqrt(1 - 3*x)) / (sqrt(x + 1)*(1 - 4*x) + sqrt(1 - 3*x)): ser := series(ogf, x, 32): seq(coeff(ser, x, n), n = 0..28);
# Alternatively:
a := proc(n) option remember; ifelse(n < 5, [1, 1, 3, 9, 28][n + 1],
((36-12*n)*a(n-4) + (30-14*n)*a(n-3) + (3*n-3)*a(n-2) + a(n-1)*(4*n-3))/n) end:
seq(a(n), n = 0..28);

Crossrefs

Cf. A202710, A001006.

Sequence in context: A022020 A195675 A170953 * A333504 A199104 A049220

Adjacent sequences: A358089 A358090 A358091 * A358093 A358094 A358095

Keyword

nonn

Author

Peter Luschny, Oct 29 2022

Status

approved