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A182015 Diagonal sums of triangle A182013. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

EXAMPLE

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

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Last modified April 23 14:15 EDT 2019. Contains 322386 sequences. (Running on oeis4.)