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 A173283 A(x) satisfies A005408(x) = A(x)/A(x^2), A005408 = odd numbers. 2
 1, 3, 8, 16, 32, 56, 96, 152, 240, 360, 536, 768, 1096, 1520, 2096, 2824, 3792, 5000, 6568, 8496, 10960, 13960, 17728, 22264, 27896, 34624, 42872, 52640, 64504, 78464, 95248, 114856, 138256, 165448, 197640, 234832, 278592, 328920, 387744, 455064 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS (1 + 3x + 5x^2 + 7x^3 + ...) = (1 + 3x + 8x^2 + 16x^3 + ...) / (1 + 3x^2 + 8x^4 + 16x^6 + ...). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA Given M = triangle A152204, odd numbers shifted down twice in every column > 0. A173283 = lim_{n->inf} M^n, the left-shifted vector considered as a sequence. a(n) = Sum_{t=0..n/2} (2*n - 4*t + 1)*a(t). - R. J. Mathar, Apr 01 2010 MAPLE A173283 := proc(n) option remember; if n = 0 then 1; else add(procname(l)*(2*n-4*l+1), l=0..n/2) ; end if; end proc: seq(A173283(n), n=0..60) ; # R. J. Mathar, Apr 01 2010 MATHEMATICA m = 40; A[_] = 1; Do[A[x_] = A[x^2] (1 + x)/(1 - x)^2 + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Feb 06 2020 *) CROSSREFS Cf. A005408, A152204. Sequence in context: A081661 A005103 A001978 * A077552 A171497 A024623 Adjacent sequences:  A173280 A173281 A173282 * A173284 A173285 A173286 KEYWORD nonn AUTHOR Gary W. Adamson, Feb 14 2010 EXTENSIONS More terms from R. J. Mathar, Apr 01 2010 STATUS approved

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)