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

Author

Emanuele Munarini, Apr 06 2012

Keywords

• nonn

Crossrefs

Cf. A182013.

Programs

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}]

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);

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).