A322417 a(n) - 2*a(n-1) = period 2: repeat [3, 0] for n > 0, a(0)=5, a(1)=13.

5, 13, 26, 55, 110, 223, 446, 895, 1790, 3583, 7166, 14335, 28670, 57343, 114686, 229375, 458750, 917503, 1835006, 3670015, 7340030, 14680063, 29360126, 58720255, 117440510, 234881023, 469762046, 939524095, 1879048190, 3758096383, 7516192766

Offset: 0

Author

Paul Curtz, Dec 07 2018

Keywords

• nonn
• easy

Comments

a(n) mod 9 = period 6: repeat [5, 4, 8, 1, 2, 7]. See A177883(n+2).

a(n+1) mod 10 = period 4: repeat [3, 6, 5, 0].

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Crossrefs

Cf. A166920, A175805, A206372, A321483.

Cf. A177883.

Programs

GAP

a:=[13,26];; for n in [3..30] do a[n]:=a[n-2]+21*2^(n-2); od; Concatenation([5],a); # Muniru A Asiru, Dec 07 2018

Mathematica

a[0] = 5; a[1] = 13; a[n_] := a[n] = a[n - 2] + 21*2^(n - 2); Array[a, 30, 0] (* Amiram Eldar, Dec 07 2018 *)
LinearRecurrence[{2, 1, -2}, {5, 13, 26}, 31] (* Jean-François Alcover, Jan 28 2019 *)

PARI

Vec((5 + 3*x - 5*x^2) / ((1 - x)*(1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Dec 07 2018

Formula

a(n) = A166920(n) + A166920(n+1) + A166920(n+2) for n >= 2.

a(n) = a(n-2) + 21*2^(n-2) for n >= 2.

a(n) = a(n-1) + A321483(n) for n > 0.

From Colin Barker, Dec 07 2018: (Start)

G.f.: (5 + 3*x - 5*x^2) / ((1 - x)*(1 + x)*(1 - 2*x)).

a(n) = 7*2^n - 2 for n even.

a(n) = 7*2^n - 1 for n odd.

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

(End)

a(2*n+1) = A206372(n). a(2*n+2) = 2*A206372(n) for n > 0.

Extensions

First formula corrected by Jean-François Alcover, Feb 01 2019