A340627 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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

Table of n, a(n) for n=0..33.

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

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

MATHEMATICA

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

PROG

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

CROSSREFS

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

Cf. also A052997.

Sequence in context: A169929 A129067 A298612 * A350520 A168155 A005735

Adjacent sequences: A340624 A340625 A340626 * A340628 A340629 A340630

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Apr 25 2021

EXTENSIONS

More terms from Michel Marcus, Apr 25 2021

New name from Jianing Song, Apr 25 2021

STATUS

approved