A001404 - OEIS

%I #17 Jun 11 2013 16:22:10

%S 1,1,1,2,2,1,4,5,2,1,9,11,5,2,1,20,25,12,5,2,1,45,57,27,12,5,2,1,102,

%T 129,62,28,12,5,2,1,231,293,141,64,28,12,5,2,1,524,665,321,146,65,28,

%U 12,5,2,1,1189,1510,729,333,148,65,28,12,5,2,1,2699,3428,1656

%N Triangle of values of 2-d recurrence.

%C The first column of the triangle (see example) appears to be A167750. [_Joerg Arndt_, Jul 09 2012]

%e Triangle starts

%e 1,

%e 1, 1,

%e 2, 2, 1,

%e 4, 5, 2, 1,

%e 9, 11, 5, 2, 1,

%e 20, 25, 12, 5, 2, 1,

%e 45, 57, 27, 12, 5, 2, 1,

%e 102, 129, 62, 28, 12, 5, 2, 1,

%e 231, 293, 141, 64, 28, 12, 5, 2, 1,

%e 524, 665, 321, 146, 65, 28, 12, 5, 2, 1,

%e 1189, 1510, 729, 333, 148, 65, 28, 12, 5, 2, 1,

%p a[ 0,0 ] := 1; for i from 1 to N do a[ i,0 ] := a[ i-1,0 ]+a[ i-1,1 ]; for j from 1 to i do a[ i,j ] := sum(a[ i-j,t ],t=0..min(j+1,N)) od; od;

%o (PARI) T(m,n)=if(m<n,0,if(m==0&&n==0,1,if(n==0,T(m-1,0)+T(m-1,1),sum(t=0,n+1,T(m-n,t))))) /* _Ralf Stephan_ */

%Y Cf. A001410.

%K tabl,nonn,easy

%O 0,4

%A _N. J. A. Sloane_ [ I have temporarily mislaid the name of the person who sent this ]

%E Sequence corrected by _Sean A. Irvine_, Jul 08 2012