A340627 a(n) = (11*2^n - 2*(-1)^n)/3 for n >= 0.

3, 8, 14, 30, 58, 118, 234, 470, 938, 1878, 3754, 7510, 15018, 30038, 60074, 120150, 240298, 480598, 961194, 1922390, 3844778, 7689558, 15379114, 30758230, 61516458, 123032918, 246065834, 492131670, 984263338, 1968526678, 3937053354, 7874106710, 15748213418, 31496426838

Offset: 0

Author

Paul Curtz, Apr 25 2021

Keywords

• nonn
• easy

Comments

Based on A112387.

Prepended with 0, 1, its difference table is

0, 1, 1, 2, 1, 4, 3, 8, ... = mix A001045(n), 2^n.

1, 0, 1, -1, 3, -1, 5, -3, ... = mix A001045(n+1), -A001045(n).

-1, 1, -2, 4, -4, 6, -8, 14, ... = mix -2^n, A084214(n+1).

2, -3, 6, -8, 10, -14, 22, -30, ... = mix 2*A001045(n+2), -a(n).

Links

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

Crossrefs

Cf. A000079, A001045, A062510, A078008, A112387.

Cf. also A052997.

Programs

Mathematica

LinearRecurrence[{1, 2}, {3, 8}, 35] (* Amiram Eldar, Apr 25 2021 *)

PARI

a(n) = (11*2^n - 2*(-1)^n)/3 \\ Felix Fröhlich, Apr 25 2021

Formula

a(n) = 2^(n+2) - A078008(n), n>=0.

a(n) = (A062510(n) = 3*A001045(n)) + A001045(n+3), n>=0.

a(0)=3, a(2*n+1) = 2*a(2*n) + 2, a(2*n+2) = 2*a(2*n+1) - 2, n>=0.

a(n) = 4*A052997(n-1) + 2, n>=2. - Hugo Pfoertner, Apr 25 2021

a(n+1) = 11*2^n - a(n) for n>=0.

a(n+3) = 33*2^n - a(n) for n>=0.

a(n+5) = 121*2^n - a(n) for n>=0.

etc.

a(n+2) = a(n) + 11*2^n for n>=0.

a(n+4) = a(n) + 55*2^n for n>=0.

a(n+6) = a(n) + 231*2^n for n>=0.

etc.

G.f.: (3 + 5*x)/(1 - x - 2*x^2). - Stefano Spezia, Apr 26 2021

E.g.f: (11*exp(2*x) - 2*exp(-x))/3. - Jianing Song, Apr 26 2021

Extensions

More terms from Michel Marcus, Apr 25 2021

New name from Jianing Song, Apr 25 2021