|
Search: id:A073149
|
|
|
| A073149 |
|
Triangle of numbers arising in recursive computation of A002212. |
|
+0
1
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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},...
|
|
PROGRAM
|
(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: A062042 A107817 A008811 this_sequence A065461 A008824 A081942
Adjacent sequences: A073146 A073147 A073148 this_sequence A073150 A073151 A073152
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jul 18 2002
|
|
|
Search completed in 0.002 seconds
|
