A182015 - OEIS

%I #12 Feb 01 2021 10:17:41

%S 1,2,5,11,26,60,145,353,884,2241,5786,15108,39941,106558,286809,

%T 777505,2121668,5822287,16059288,44494738,123782207,345615047,

%U 968211110,2720561790,7665640267,21654105734,61312389677,173978404587,494667697706,1409099662020

%N Diagonal sums of triangle A182013.

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

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

%F 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).

%t 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}]

%o (Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)),x^n)/(n+1);

%o makelist(sum((n-i+1)*M(i),i,0,n)-sum((n-2*i)*M(i),i,0,floor(n/2)),n,0,30);

%Y Cf. A182013.

%K nonn

%O 0,2

%A _Emanuele Munarini_, Apr 06 2012