

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
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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



