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A073149
Triangle of numbers arising in recursive computation of A002212.
0
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
0,3
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.
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.
EXAMPLE
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},...
PROG
(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))))
CROSSREFS
T(n, 0)=A002212(n). T(n, n)=A045868(n).
Sequence in context: A144678 A309678 A279225 * A065461 A008824 A261616
KEYWORD
easy,nonn,tabl
AUTHOR
Paul D. Hanna, Jul 18 2002
STATUS
approved