A159974 Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.

1, 1, 1, 2, 1, 2, 3, 2, 2, 5, 4, 3, 4, 5, 12, 5, 4, 6, 10, 12, 28, 6, 5, 8, 15, 24, 28, 65, 7, 6, 10, 20, 36, 56, 65, 151, 8, 7, 12, 25, 48, 84, 130, 151, 351, 9, 8, 14, 30, 60, 112, 195, 302, 351, 816, 10, 9, 16, 35, 72, 140, 260, 453, 702, 816, 1897

Offset

2,4

Comments

Row sums = A034943 starting (1, 2, 5, 12, 28, 65, 151, 351, ...).

As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

A034943 starting (1, 2, 5, 12, 28, ...) = the INVERT transform of (1, 1, 2, 3, 4, 5, ...).

Links

Table of n, a(n) for n=2..67.

Formula

Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, ...) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, ...) as the main diagonal and the rest zeros.

Example

First few rows of the triangle:
   1;
   1, 1;
   2, 1,  2;
   3, 2,  2,  5;
   4, 3,  4,  5, 12;
   5, 4,  6, 10, 12,  28;
   6, 5,  8, 15, 24,  28,  65;
   7, 6, 10, 20, 36,  56,  65, 151;
   8, 7, 12, 25, 48,  84, 130, 151, 351;
   9, 8, 14, 30, 60, 112, 195, 302, 351, 816;
  10, 9, 16, 35, 72, 140, 260, 453, 702, 816, 1897;
  ...
Example: row 6 = (4, 3, 4, 5, 12) = termwise products of (1, 1, 2, 5, 12) and (4, 3, 2, 1, 1).

Crossrefs

Cf. A034943.

Sequence in context: A172366 A132148 A237829 * A143866 A155002 A182413

Adjacent sequences: A159971 A159972 A159973 * A159975 A159976 A159977

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 28 2009

Status

approved