A073149 Triangle of numbers arising in recursive computation of A002212.

1, 1, 2, 3, 4, 7, 10, 13, 16, 26, 36, 46, 55, 65, 101, 137, 173, 203, 233, 269, 406, 543, 680, 788, 888, 996, 1133, 1676, 2219, 2762, 3173, 3533, 3893, 4304, 4847, 7066, 9285, 11504, 13133, 14503, 15799, 17169, 18798, 21017, 30302, 39587, 48872, 55529

Offset: 0

Author

Paul D. Hanna, Jul 18 2002

Keywords

• easy
• nonn
• tabl

Comments

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

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

Examples

			T(5,3)=T(5,2)+T(3,0)T(5-2,0)=203+10*3=233.
{1}, {1,2}, {3,4,7}, {10,13,16,26}, {36,46,55,65,101},...
		

Crossrefs

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

Programs

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))))

Formula

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.

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.