

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, 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
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OFFSET

2,4


COMMENTS

Row sums = A034943 starting (1, 2, 5, 12, 28, 65, 151, 351, ...).
As a property of eigentriangles, sum of nth 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



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).


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KEYWORD



AUTHOR



STATUS

approved



