|
%I #12 Mar 22 2022 10:00:57
%S 1,2,4,5,9,14,18,28,38,56,70,106,131,167,237,293,433,523,613,753,1046,
%T 1283,1869,2219,2543,2893,3479,4762,5808,8374,9839,11099,12359,13824,
%U 16390,22198
%N Triangle of numbers relating two sequences (A073157 and A073155).
%F Triangle {a(n, k), n >= 0, 0<=k<=n} defined by: a(0, 0)=1, a(n, 0)=A073157(n), a(n, n)=A073155(n+1), a(n, 0)=a(n-1, n-1) + a(n-2, n-2), a(n, k)=sum{j=0..k} A073157(j) * A073157(n-j).
%F G.f.: Sum_{n>=0, 0<=k<=n} a(n, k) x^n y^k = A(x*y)(A(x) - y A(x*y))/(1 - y) where A(x) = (1 - (1 - 4 x (1 + x)^2)^(1/2))/(2 x (1 + x)) is the o.g.f. for A073157. - _David Callan_, Aug 16 2006
%e a(4,0)=a(3,3)+a(2,2)=56+14=70.
%e a(5,2)=A073157(0)*A073157(5)+A073157(1)*A073157(4)+A073157(2)*A073157(3)= 1*293+2*70+5*18=523.
%e Rows:
%e {1};
%e {2,4};
%e {5,9,14};
%e {18,28,38,56};
%e {70,106,131,167,237};
%e {293,433,523,613,753,1046};
%e {1283,1869,2219,2543,2893,3479,4762};
%e ...
%Y Cf. A073153, A073155, A073156, A073157, A073152.
%K easy,nonn,tabl
%O 0,2
%A _Paul D. Hanna_, Jul 29 2002
|
