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A130460 Infinite lower triangular matrix,(1,0,0,0,...) in the main diagonal and (1,2,3,...) in the subdiagonal. 4
1, 1, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Given M = the infinite lower triangular matrix A130460 and V = any nonzero sequence with initial term "k", M*V = [k,...(1, 2, 3,...) dot (V)]. Example: say V = the sequence of primes as a Vector: [2, 3, 5, 7...]. Then M*V = [2, 2, 6, 15, 28, 55, 78,...]; since k = 2 and (1, 2, 3,...) dot (2, 3, 5, 7,...) = 2, 6, 15, 28, 55,...]. Given V = [1, 2, 3,...], then M*V = [1, 1, 4, 9, 16, 25, 36,...]. Repeated iterates of M*V = ANS, then M*ANS, etc..., quickly generates a sequence tending to k * [1, 1, 2, 6, 24, 120,...]. Since k = 2 in [2, 3, 5, 7,...] repeated iterates of the operation tends to [2, 2, 4, 12, 48, 240,...] = 2 * [1, 1, 2, 6, 24, 120,...].

LINKS

Table of n, a(n) for n=1..78.

FORMULA

A natural number operator as an infinite lower triangular matrix M. (1,0,0,0,...) in the main diagonal, (1,2,3,...) in the subdiagonal and the rest zeros.

EXAMPLE

First few rows of the triangle are:

1;

1, 0;

0, 2, 0;

0, 0, 3, 0;

0, 0, 0, 4, 0;

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

...

CROSSREFS

Cf. A130461, A130476, A130477, A130478.

Sequence in context: A083927 A154724 A232747 * A132440 A218272 A134402

Adjacent sequences:  A130457 A130458 A130459 * A130461 A130462 A130463

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, May 28 2007

EXTENSIONS

a(5) corrected by Gionata Neri, Jun 22 2016

STATUS

approved

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Last modified January 25 01:49 EST 2020. Contains 331229 sequences. (Running on oeis4.)