A096584 -id:A096584 - cp's OEIS frontend

A096585 Main diagonal of the square array A096583, in which the n-th diagonal equals the convolution of the n-th row with the antidiagonal sums (A096584).

1, 3, 8, 20, 44, 96, 186, 372, 678, 1252, 2194, 3884, 6502, 11102, 18194, 29966, 47988, 77300, 121194, 191132, 294986, 456368, 694516, 1058334, 1588762, 2388128, 3545232, 5263138, 7733564, 11356850, 16526932, 24036988, 34684020, 49989938

Offset: 0

Paul D. Hanna, Jun 28 2004

nonn

Forms the partial sums of A096584 (the antidiagonal sums of array A096583).

Cf. A096583, A096584.

PARI

A096583 Symmetric square array T(n,k)=T(k,n), read by antidiagonals, such that the n-th diagonal equals the convolution of the n-th row with the antidiagonal sums, with T(0,n)=1, for n>=0.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 8, 7, 1, 1, 9, 16, 16, 9, 1, 1, 11, 23, 20, 23, 11, 1, 1, 13, 35, 44, 44, 35, 13, 1, 1, 15, 46, 69, 44, 69, 46, 15, 1, 1, 17, 62, 99, 108, 108, 99, 62, 17, 1, 1, 19, 77, 147, 179, 96, 179, 147, 77, 19, 1, 1, 21, 97, 206, 272, 248, 248, 272, 206, 97, 21

Offset: 0

Paul D. Hanna, Jun 28 2004

The main diagonal (A096585) equals the partial sums of the antidiagonal sums (A096584).

			Antidiagonal sums are A096584 =
[1,2,5,12,24,52,90,186,306,574,...];
convolution of antidiagonal sums and first row yields main diagonal:
A096585 = [1,3,8,20,44,96,186,372,678,...];
convolution of antidiagonal sums and second row yields secondary
diagonal:
[1,5,16,44,108,248,530,1088,2138,4068,...].
Rows begin:
[1,1,1,1,1,1,1,1,1,...],
[1,3,5,7,9,11,13,15,17,...],
[1,5,8,16,23,35,46,62,77,...],
[1,7,16,20,44,69,99,147,206,...],
[1,9,23,44,44,108,179,272,379,...],
[1,11,35,69,108,96,248,429,669,...],
[1,13,46,99,179,248,186,530,965,...],
[1,15,62,147,272,429,530,372,1088,...],
[1,17,77,206,379,669,965,1088,678,...],...

Cf. A096584, A096585.

T(n,k)=if(n<0 || k<0,0,if(n==0 || k==0,1,if(n>k, sum(j=0,k,T(n-k,j)*sum(i=0,k-j,T(k-j-i,i))), sum(j=0,n,T(k-n,j)*sum(i=0,n-j,T(n-j-i,i))););))

cp's OEIS Frontend

A096585 Main diagonal of the square array A096583, in which the n-th diagonal equals the convolution of the n-th row with the antidiagonal sums (A096584).

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