A022110 Fibonacci sequence beginning 1, 20.

1, 20, 21, 41, 62, 103, 165, 268, 433, 701, 1134, 1835, 2969, 4804, 7773, 12577, 20350, 32927, 53277, 86204, 139481, 225685, 365166, 590851, 956017, 1546868, 2502885, 4049753, 6552638, 10602391, 17155029, 27757420, 44912449, 72669869, 117582318, 190252187

Offset

0,2

Comments

a(n-1) = Sum(P(20;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1) = 19. These are the SW-NE diagonals in P(20;n,k), the (20,1) Pascal triangle. Cf. A093645 for the (10,1) Pascal triangle. Observation by Paul Barry, Apr 29 2004. Proof via recursion relations and comparison of inputs.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (1,1).

Formula

a(n) = a(n-1)+a(n-2), n >= 2, a(0) = 1, a(1) = 20.

G.f.: (1+19*x)/(1-x-x^2).

Mathematica

a={}; b=1; c=20; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
LinearRecurrence[{1, 1}, {1, 20}, 35] (* Paolo Xausa, Feb 22 2024 *)

Prog

(Magma) a0:=1; a1:=20; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // Bruno Berselli, Feb 12 2013

Crossrefs

a(n) = A109754(19, n+1) = A101220(19, 0, n+1).

Sequence in context: A176241 A075034 A363770 * A041808 A041810 A042855

Adjacent sequences: A022107 A022108 A022109 * A022111 A022112 A022113

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved