A022109 Fibonacci sequence beginning 1, 19.

1, 19, 20, 39, 59, 98, 157, 255, 412, 667, 1079, 1746, 2825, 4571, 7396, 11967, 19363, 31330, 50693, 82023, 132716, 214739, 347455, 562194, 909649, 1471843, 2381492, 3853335, 6234827, 10088162, 16322989, 26411151, 42734140, 69145291, 111879431, 181024722

Offset

0,2

Comments

a(n-1) = Sum(P(19;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=18. These are the SW-NE diagonals in P(19;n,k), the (19,1) 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) = 19.

G.f.: (1+18*x)/(1-x-x^2).

Mathematica

LinearRecurrence[{1, 1}, {1, 19}, 35] (* Paolo Xausa, Feb 22 2024 *)

Prog

(Magma) a0:=1; a1:=19; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // Bruno Berselli, Feb 12 2013

Crossrefs

a(n) = A109754(18, n+1) = A101220(18, 0, n+1).

Sequence in context: A241849 A054304 A151979 * A041730 A041732 A041728

Adjacent sequences: A022106 A022107 A022108 * A022110 A022111 A022112

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved