A182015 Diagonal sums of triangle A182013.

1, 2, 5, 11, 26, 60, 145, 353, 884, 2241, 5786, 15108, 39941, 106558, 286809, 777505, 2121668, 5822287, 16059288, 44494738, 123782207, 345615047, 968211110, 2720561790, 7665640267, 21654105734, 61312389677, 173978404587, 494667697706, 1409099662020

Offset

0,2

Links

Table of n, a(n) for n=0..29.

Formula

a(n) = sum(sum(M(i),i=k..n-k),k=0..n), where the M(n)'s are the Motzkin numbers.

a(n) = sum((n-i+1)*M(i),i=0..n) - sum((n-2*i)*M(i),i=0..floor(n/2)).

G.f.: (1-x+x*sqrt(1-2*x-3*x^2)-sqrt(1-2*x^2-3*x^4))/(2*x^3*(1-x)^2).

Mathematica

M[n_]:=If[n==0, 1, Coefficient[(1+x+x^2)^(n+1), x^n]/(n+1)]; Table[Sum[(n-i+1)M[i], {i, 0, n}]-Sum[(n-2i)M[i], {i, 0, Floor[n/2]}], {n, 0, 30}]

Prog

(Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)), x^n)/(n+1);
makelist(sum((n-i+1)*M(i), i, 0, n)-sum((n-2*i)*M(i), i, 0, floor(n/2)), n, 0, 30);

Crossrefs

Cf. A182013.

Sequence in context: A291930 A238437 A191692 * A124217 A095981 A247471

Adjacent sequences: A182012 A182013 A182014 * A182016 A182017 A182018

Keyword

nonn

Author

Emanuele Munarini, Apr 06 2012

Status

approved