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A157905 Triangle read by rows, T(n,k) = A000055(n-k) * (A157904 * 0^(n-k)) 2
1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 2, 1, 2, 4, 8, 3, 2, 2, 4, 8, 17, 6, 3, 4, 4, 8, 17, 36, 11, 6, 6, 8, 8, 17, 36, 78, 23, 11, 12, 12, 16, 17, 36, 78, 170, 47, 23, 22, 24, 24, 34, 36, 78, 170, 375, 106, 47, 46, 44, 48, 51, 72, 78, 170, 375, 833 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Row sums = A157904: (1, 2, 4, 8, 17, 36, 78, 170, 375,...). As a property of eigentriangles, sum of n-th row terms = rightmost term of next row. Left border = A000055.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

Triangle read by rows, T(n,k) = A000055(n-k) * (A157904 * 0^(n-k)). A000055(n-k) = an infinite lower triangular matrix with A000055 in every column: (1, 1, 1, 1, 2, 3, 6, 11, 23,...). (A157904 * 0^(n-k)) = a matrix with A157904 as the diagonal and the rest zeros.

EXAMPLE

First few rows of the triangle =

1;

1, 1;

1, 1, 2;

1, 1, 2, 4;

2, 1, 2, 4, 8;

3, 2, 2, 4, 8, 17;

6, 3, 4, 4, 8, 17, 36;

11, 6, 6, 8, 8, 17, 36, 78;

23, 11, 12, 12, 16, 17, 36, 78, 170;

47, 23, 22, 24, 24, 34, 36, 78, 170, 375;

106, 47, 46, 44, 48, 51, 72, 78, 170, 375, 833;

235, 106, 94, 92, 88, 102, 108, 156, 170, 375, 833, 1870;

...

Row 5 = (3, 2, 2, 4, 8, 17) = termwise products of (3, 2, 1, 1, 1, 1) and (1, 1, 2, 4, 8, 17).

CROSSREFS

Cf. A000055, A157904

Sequence in context: A097853 A160266 A023504 * A260931 A293819 A027113

Adjacent sequences:  A157902 A157903 A157904 * A157906 A157907 A157908

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Mar 08 2009

STATUS

approved

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Last modified October 18 05:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)