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A171608 Triangle by columns, T(n,k); (...n, (n+1)) preceded by (n-1) zeros, as an infinite lower triangular matrix 5
1, 2, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let the triangle = M as an infinite lower triangular matrix.

.

M * (1, 2, 3,...) = A002620: (1, 2 4, 6, 9, 12, 16, 20,...)

M * (1, 3, 5,...) = A084265: (1, 2, 6, 9, 15, 20, 28, 35,...)

M * (1, 3, 6,...) = A028724: (1, 2, 6, 9, 18, 24, 40, 50, ...)

Lim_{n->inf.} M^n = A171609: (1, 2, 4, 6, 12, 16, 24, 30, ...)

LINKS

Table of n, a(n) for n=1..54.

FORMULA

Triangle by columns, T(n,k); (...n, (n+1)) preceded by (n-1) zeros, as an infinite lower triangular matrix

EXAMPLE

First few rows of the triangle =

1;

2, 0;

0, 2, 0;

0, 3, 0, 0;

0, 0, 3, 0, 0;

0, 0, 4, 0, 0, 0;

0, 0, 0, 4, 0, 0, 0;

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

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

0, 0, 0, 0, 6, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0;

0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0;

...

CROSSREFS

Cf. A002620, A084265, A028724, A171608

Sequence in context: A216921 A280285 A033719 * A024164 A138805 A061897

Adjacent sequences:  A171605 A171606 A171607 * A171609 A171610 A171611

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Dec 12 2009

STATUS

approved

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Last modified February 21 16:54 EST 2018. Contains 299414 sequences. (Running on oeis4.)