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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A091492 Triangle, read by rows, generated recursively and related to partitions.

Original entry on oeis.org

1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 1, 1, 3, 1, 0, 0, 0, 0, 1, 1, 3, 2, 0, 0, 0, 0, 0, 1, 1, 4, 3, 0, 0, 0, 0, 0, 0, 1, 1, 4, 4, 1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 5, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 7, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 8, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Paul D. Hanna, Jan 16 2004

Keywords

Comments

Excluding the leading zeros, the columns are related to partitions. The 3rd column lists A001399 (partitions of n into at most 3 parts). The 4th column lists A001400 (partitions of n into at most 4 parts). The 5th column lists A001401 (partitions of n into at most 5 parts). The 6th column is A091498. Row sums are A091493. The number of nonzero terms in each row is A091497.

Examples

			T(12,3) = 7 = (4)*1+(3)*1 = T(9,2)*T(2,1)+T(9,3)*T(3,0) = Sum T(9,j)*T(j,3-j) {j=2..3}.
Rows begin:
{1},
{1,1},
{1,1,0},
{1,1,1,0},
{1,1,1,0,0},
{1,1,2,0,0,0},
{1,1,2,1,0,0,0},
{1,1,3,1,0,0,0,0},
{1,1,3,2,0,0,0,0,0},
{1,1,4,3,0,0,0,0,0,0},
{1,1,4,4,1,0,0,0,0,0,0},
{1,1,5,5,1,1,0,0,0,0,0,0},
{1,1,5,7,2,1,0,0,0,0,0,0,0},
{1,1,6,8,3,2,0,0,0,0,0,0,0,0},
{1,1,6,10,5,3,0,0,0,0,0,...
{1,1,7,12,6,5,0,0,0,0,0,...
{1,1,7,14,9,7,1,0,0,0,0,...
{1,1,8,16,11,10,2,0,0,0,...
{1,1,8,19,15,13,3,2,0,0,...
{1,1,9,21,18,18,5,2,0,0,...
{1,1,9,24,23,23,8,4,0,0,...
{1,1,10,27,27,30,11,6,0,...
{1,1,10,30,34,37,17,10,0,...

Crossrefs

Cf. A001399, A001400, A001401, A091493, A091497, A091498.

Programs

  • PARI
    T(n,k)=if(k>n || n<0 || k<0,0,if(k<=1 || (k==n && n<2),1, sum(j=(k+1)\2,min(n-k,k),T(n-k,j)*T(j,k-j)););)

Formula

T(n, k)=Sum T(n-k, j)*T(j, k-j) {j=[(k+1)/2]..min(k, n-k)}, with T(0, 0)=1, T(n, 0)=1, T(1, 1)=1.

A091493 Row sums of triangle A091492.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 11, 14, 17, 21, 26, 32, 40, 49, 62, 75, 93, 113, 140, 170, 209, 255, 313, 383, 468, 567, 693, 840, 1022, 1235, 1503, 1816, 2209, 2667, 3248, 3923, 4754, 5743, 6949, 8384, 10126, 12195, 14717, 17726, 21369, 25732, 31020, 37393
Offset: 0

Views

Author

Paul D. Hanna, Jan 16 2004

Keywords

Crossrefs

Cf. A091492, A091497.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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