The On-Line Encyclopedia of Integer Sequences (OEIS)

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A157424

Triangle read by rows, A157423 * (A052284 * 0^(n-k))
(history; published version)

#7 by Andrey Zabolotskiy at Tue Dec 26 12:29:29 EST 2023

STATUS

editing

approved

#6 by Andrey Zabolotskiy at Tue Dec 26 12:29:27 EST 2023

NAME

Triangle read by rows, A157423 * ((A052284 * 0^(n-k))

FORMULA

Triangle read by rows, A157423 * ((A052284 * 0^(n-k)). A157423 = an infinite lower triangular matrix with A005171 in every column. ((A052284 * 0^(n-k)) = an infinite lower triangular matrix with A052284: (1, 1, 1, 1, 2, 3, 5, 7, 11, 17, 27,...) as the main diagonal and the rest zeros.

STATUS

approved

editing

#5 by Alois P. Heinz at Tue Aug 06 17:32:07 EDT 2019

STATUS

editing

approved

#4 by Alois P. Heinz at Tue Aug 06 17:32:04 EDT 2019

COMMENTS

Row sums = A052284 starting with offset at n=1: (1, 1, 1, 2, 3, 5, 7, 11, 17,...). As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

STATUS

approved

editing

#3 by R. J. Mathar at Thu Apr 05 17:26:55 EDT 2012

STATUS

editing

approved

#2 by R. J. Mathar at Thu Apr 05 17:26:46 EDT 2012

AUTHOR

_Gary W. Adamson _ & _Mats Granvik (qntmpkt(AT)yahoo.com), _, Feb 28 2009

STATUS

approved

editing

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Triangle read by rows, A157423 * ((A052284 * 0^(n-k))

DATA

1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 0, 1, 0, 1, 0, 0, 5, 1, 0, 1, 0, 1, 0, 0, 7, 1, 1, 0, 1, 0, 3, 0, 0, 11, 1, 1, 1, 0, 2, 0, 5, 0, 0, 0, 17, 0, 1, 1, 1, 0, 3, 0, 7, 0, 0, 27, 1, 0, 1, 1, 2, 0, 5, 0, 11, 0, 0, 40

OFFSET

1,15

COMMENTS

Row sums = A052284 starting with offset 1: (1, 1, 1, 2, 3, 5, 7, 11, 17,...). As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.

FORMULA

EXAMPLE

First few rows of the triangle =

1;

0, 1;

0, 0, 1;

1, 0, 0, 1;

0, 1, 0, 0, 2;

1, 0, 1, 0, 0, 3;

0, 1, 0, 1, 0, 0, 5;

1, 0, 1, 0, 2, 0, 0, 7;

1, 1, 0, 1, 0, 3, 0, 0, 11;

1, 1, 1, 0, 2, 0, 5,0, 0, 17;

0, 1, 1, 1, 0, 3, 0, 7, 0, 0, 27;

1, 0, 1, 1, 2, 0, 5, 0, 11, 0, 0, 40;

0, 1, 0, 1, 2, 3, 0, 7, 0, 17, 0, 0, 61;

1, 0, 1, 0, 2, 3, 5, 0, 11, 0, 27, 0, 0, 92;

...

Example: row 5 = (0, 1, 0, 0, 2) = termwise products of (0, 1, 0, 0, 1) and

(1, 1, 1, 1, 2); where (0, 1, 0, 0, 2) = row 5 of triangle A157423 and

(1, 1, 1, 1, 2) = the first 5 terms of A052284.

CROSSREFS

Cf. A157423, A005171, A052284

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson & Mats Granvik (qntmpkt(AT)yahoo.com), Feb 28 2009

STATUS

approved