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A159934 Triangle, row sums = d(n): M * Q; where M = an infinite lower Toeplitz matrix with A159933 in every column. Q = an infinite lower triangular matrix with d(n) shifted: (1, 1, 2, 2, 3, 2, 4,...) as the main diagonal and the rest zeros. 2
1, 1, 1, -1, 1, 2, 0, -1, 2, 2, -1, 0, -2, 2, 3, 2, -1, 0, -2, 3, 2, -1, 2, -2, 0, -3, 2, 4, -1, -1, 4, -2, 0, -2, 4, 2, 3, -1, -2, 4, -3, 0, -4, 2, 4, -4, 3, -2, -2, 6, -2, 0, -2, 4, 3, 2, -4, 6, -2, -3, 4, -4, 0, -4, 3, 4 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Triangle = an infinite lower triangular Toeplitz matrix with the INVERTi

transform of d(n) in every column; i.e. A159933: (1, 1, -1, 0, -1, 2, -1,...). Row sums of the resulting eigentriangle of d(n) = d(n).

Sum of n-th row terms = rightmost term of next row.

Right border = d(n) shifted.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

First few rows of the triangle =

1;

1, 1;

-1, 1, 2;

0, -1, -2, 2;

-1, 0, -2, 2, 3;

2, -1, 0, -2, 3, 2;

-1, 2, -2, 0, -3, 2, 4;

-1, -1, 4, -2, 0, -2, 4, 2;

3, -1, -2, 4, -3, 0, -4, 2, 4;

-4, 3, -2, -2, 6, -2, 0, -2, 4, 3;

2, -4, 6, -2, -3, 4, -4, 0, -4, 3, 4;

2, 2, -8, 6, -3, -2, 8, -2, 0, -3, 4, 2;

-3, 2, 4, -8, 9, -2, -4, 4, -4, 0, -4, 2, 6;

0, -3, 4, 4, -12, 6, -4, -2, 8, -3, 0, -2, 6, 2;

0, 0, -6, 4, 6, -8, 12, -2, -4, 6, -4, 0, -6, 2, 4;

6, 0, 0, -6, 6, 4, -16, 6, -4, -3, 8, -2, 0, -2, 4, 4;

...

Example: row 6 = (2, -1, 0, -2, 3, 2) = termwise products of

(2, -1, 0, -1, 1, 1) and (1, 1, 2, 2, 3, 2); with dot product sum = 4 = d(6).

CROSSREFS

A159933

Sequence in context: A292475 A316716 A145462 * A229204 A067460 A159855

Adjacent sequences:  A159931 A159932 A159933 * A159935 A159936 A159937

KEYWORD

tabl,sign

AUTHOR

Gary W. Adamson, Apr 26 2009

STATUS

approved

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Last modified October 21 02:33 EDT 2018. Contains 316405 sequences. (Running on oeis4.)