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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 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.)