A073149 - OEIS

%I #7 Jun 13 2017 21:44:56

%S 1,1,2,3,4,7,10,13,16,26,36,46,55,65,101,137,173,203,233,269,406,543,

%T 680,788,888,996,1133,1676,2219,2762,3173,3533,3893,4304,4847,7066,

%U 9285,11504,13133,14503,15799,17169,18798,21017,30302,39587,48872,55529

%N Triangle of numbers arising in recursive computation of A002212.

%C Related to restricted hexagonal polyominoes with n cells (A002212) and catafusenes (A045868).

%C Only T(n,k) for 0<=k<=n are listed since T(n,k)=T(n,n) if k>n.

%F G.f.: Sum_{n>=0, k>=0} T(n, k)*y^k*x^n = A(x)*A(xy)/(1-y) where A(x) is g.f. of A002212.

%F T(0, k)=T(1, 0)=1. T(n+1, 0)=T(n, 0)+T(n, n), n>0. T(n, k)=T(n, k-1)+T(k, 0)T(n-k, 0), k>0. T(n, k)=T(n, n), k>n.

%e T(5,3)=T(5,2)+T(3,0)T(5-2,0)=203+10*3=233.

%e {1}, {1,2}, {3,4,7}, {10,13,16,26}, {36,46,55,65,101},...

%o (PARI) T(n,k)=if(k<0 || n<0,0,if(n==0,1,if(k==0,T(n-1,0)+if(n>1,T(n-1,n-1)),T(n,k-1)+T(k,0)*T(n-k,0))))

%Y T(n, 0)=A002212(n). T(n, n)=A045868(n).

%K easy,nonn,tabl

%O 0,3

%A _Paul D. Hanna_, Jul 18 2002