A372242 a(n) = 10*Fibonacci(n) + (-1)^n.

1, 9, 11, 19, 31, 49, 81, 129, 211, 339, 551, 889, 1441, 2329, 3771, 6099, 9871, 15969, 25841, 41809, 67651, 109459, 177111, 286569, 463681, 750249, 1213931, 1964179, 3178111, 5142289, 8320401, 13462689, 21783091, 35245779, 57028871, 92274649, 149303521, 241578169

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,2,1).

Formula

Floor(a(n+2)/10) = A052952(n).

a(n) = 1 + A153382(n).

a(n) = 2*A371843(n) - (-1)^n.

a(n) = A022093(n) + (-1)^n.

G.f.: -(9*x^2+9*x+1)/((x+1)*(x^2+x-1)).

a(0) = 1. a(n) = -a(n-1) + 10*A000045(n+1) for n >= 1.

a(n) = a(n-4) + (2*A280154(n-2) = 5*A022112(n-3) = 10*A000032(n-2)) for n >= 4.

Example

a(0) = 10*0 + 1 =  1,
a(1) = 10*1 - 1 =  9,
a(2) = 10*1 + 1 = 11,
a(3) = 10*2 - 1 = 19.

Mathematica

LinearRecurrence[{0, 2, 1}, {1, 9, 11}, 50] (* Paolo Xausa, May 20 2024 *)

Crossrefs

Cf. A000045, A022093, A153382, A052952, A371843.

Cf. A000032, A022112, A280154.

Sequence in context: A299971 A090771 A329279 * A284295 A284294 A195572

Adjacent sequences: A372239 A372240 A372241 * A372243 A372244 A372245

Keyword

nonn,easy

Author

Paul Curtz, Apr 23 2024

Status

approved