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 A207613 Triangle of coefficients of polynomials v(n,x) jointly generated with A207612; see Formula section. 3
 1, 2, 2, 3, 4, 4, 5, 8, 8, 8, 8, 16, 20, 16, 16, 13, 30, 44, 48, 32, 32, 21, 56, 92, 112, 112, 64, 64, 34, 102, 188, 256, 272, 256, 128, 128, 55, 184, 372, 560, 672, 640, 576, 256, 256, 89, 328, 724, 1184, 1552, 1696, 1472, 1280, 512, 512, 144, 580, 1384 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Only column 1 contains odd numbers. column 1:  A000045 (Fibonacci sequence) row sums:  A002878 (bisection of Lucas sequence) top edge:  A000079 (powers of 2) LINKS FORMULA u(n,x) = u(n-1,x) + v(n-1,x), v(n,x) = u(n-1,x) + 2x*v(n-1,x) + 1, where u(1,x) = 1, v(1,x) = 1. With offset 0, the Riordan array ((1 + z)/(1 - z - z^2), 2*z*(1 - z)/(1 - z - z^2)) with o.g.f. (1 + z)/(1 - z - z^2 - x*(2*z - 2*z^2)) = 1 + (2 + 2*x)*z + (3 + 4*x + 4*x^2)*z^2 + .... - Peter Bala, Dec 30 2015 EXAMPLE First five rows:   1   2  2   3  4  4   5  8  8  8   8 16 20 16 16 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + v[n - 1, x] v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1 Table[Factor[u[n, x]], {n, 1, z}] Table[Factor[v[n, x]], {n, 1, z}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]    (* A207612 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A207613 *) CROSSREFS A000045 (column 1), A000079 (main diagonal), A002878 (row sums). Cf. A207612, A208510. Sequence in context: A097793 A015742 A015754 * A321424 A289677 A113967 Adjacent sequences:  A207610 A207611 A207612 * A207614 A207615 A207616 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Feb 19 2012 STATUS approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)