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A001404 Triangle of values of 2-d recurrence.

%I A001404 #17 Jun 11 2013 16:22:10
%S A001404 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 A001404 129,62,28,12,5,2,1,231,293,141,64,28,12,5,2,1,524,665,321,146,65,28,
%U A001404 12,5,2,1,1189,1510,729,333,148,65,28,12,5,2,1,2699,3428,1656
%N A001404 Triangle of values of 2-d recurrence.
%C A001404 The first column of the triangle (see example) appears to be A167750. [_Joerg Arndt_, Jul 09 2012]
%e A001404 Triangle starts
%e A001404 1,
%e A001404 1, 1,
%e A001404 2, 2, 1,
%e A001404 4, 5, 2, 1,
%e A001404 9, 11, 5, 2, 1,
%e A001404 20, 25, 12, 5, 2, 1,
%e A001404 45, 57, 27, 12, 5, 2, 1,
%e A001404 102, 129, 62, 28, 12, 5, 2, 1,
%e A001404 231, 293, 141, 64, 28, 12, 5, 2, 1,
%e A001404 524, 665, 321, 146, 65, 28, 12, 5, 2, 1,
%e A001404 1189, 1510, 729, 333, 148, 65, 28, 12, 5, 2, 1,
%p A001404 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 A001404 (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 A001404 Cf. A001410.
%K A001404 tabl,nonn,easy
%O A001404 0,4
%A A001404 _N. J. A. Sloane_ [ I have temporarily mislaid the name of the person who sent this ]
%E A001404 Sequence corrected by _Sean A. Irvine_, Jul 08 2012