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 A098703 a(n) = (3^n + phi^(n-1) + (-phi)^(1-n)) / 5, where phi denotes the golden ratio A001622. 5
 0, 1, 2, 6, 17, 50, 148, 441, 1318, 3946, 11825, 35454, 106328, 318929, 956698, 2869950, 8609617, 25828474, 77484812, 232453449, 697358750, 2092073666, 6276216817, 18828643686, 56485920112, 169457742625, 508373199218, 1525119551286 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Sums of antidiagonals of A090888; Partial sums of A099159; a(n) = A000045(n) + A094688(n-1); For n > 2, a(n) = 3a(n-1) - A000045(n-3); For n > 3, a(n) = 3^2a(n-2) - A000285(n-4); For n > 4, a(n) = 3^3a(n-3) - A022383(n-5); Lim_{n -> oo} a(n) / a(n-1) = 3. a(n) = A101220(1,3,n). - Ross La Haye, Dec 15 2004 Form an array with m(0,n) = A000045(n), the Fibonacci numbers, and m(i,j) = Sum_{k 1. - Ross La Haye, Aug 20 2005 Binomial transform of A052964 beginning 0,1,0,3,1,10,... - Ross La Haye, May 31 2006 EXAMPLE a(2) = 2 because 3^2 = 9, Luc(1) = 1 and (9 + 1) / 5 = 2. MATHEMATICA f[n_] := (3^n + Fibonacci[n] + Fibonacci[n - 2])/5; Table[ f[n], {n, 0, 27}] (* Robert G. Wilson v, Nov 04 2004 *) LinearRecurrence[{4, -2, -3}, {0, 1, 2}, 30] (* Jean-François Alcover, Feb 17 2018 *) PROG (MAGMA) I:=[0, 1, 2]; [n le 3 select I[n] else 4*Self(n-1)-2*Self(n-2)-3*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 18 2018 CROSSREFS Cf. A001622, A000032, A000045, A090888, A099159, A094688, A000285, A022383, A000244. Sequence in context: A173993 A270863 A027914 * A025272 A148447 A148448 Adjacent sequences:  A098700 A098701 A098702 * A098704 A098705 A098706 KEYWORD nonn,changed AUTHOR Ross La Haye, Oct 27 2004 EXTENSIONS More terms from Robert G. Wilson v, Nov 04 2004 More terms from Ross La Haye, Dec 21 2004 STATUS approved

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Last modified May 18 07:26 EDT 2021. Contains 343995 sequences. (Running on oeis4.)