A344109 a(n) = (5*2^n + 7*(-1)^n)/3.

4, 1, 9, 11, 29, 51, 109, 211, 429, 851, 1709, 3411, 6829, 13651, 27309, 54611, 109229, 218451, 436909, 873811, 1747629, 3495251, 6990509, 13981011, 27962029, 55924051, 111848109, 223696211, 447392429, 894784851, 1789569709, 3579139411, 7158278829, 14316557651, 28633115309, 57266230611, 114532461229, 229064922451

Offset

0,1

Links

Table of n, a(n) for n=0..37.

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

Formula

a(n+1) = 5*2^n - a(n) for n >= 0, with a(0) = 4.

a(n+2) = 5*2^n + a(n) for n >= 0, with a(0) = 4, a(1) = 1.

a(n+3) = 15*2^n - a(n) for n >= 0, with a(0) = 4, a(1) = 1, a(2) = 9.

a(n) = A001045(n+2) + A154879(n).

a(2*n+1) = A321421(n).

a(n) = a(n-1) + 2*a(n-2) for n >= 2. - Pontus von Brömssen, May 09 2021

G.f.: (4 - 3*x)/(1 - x - 2*x^2). - Stefano Spezia, May 10 2021

a(n) = 2*A014551(n) - A001045(n).

a(n) = abs(A156550(n)) - (-1)^n.

a(n+3) = a(n) + 7*A084214(n+1) for n >= 0, with a(0) = 4.

a(n) = 5*A001045(n+1) - A084214(n+1) for n >= 0.

a(n) = A084214(n+1) + 3*(-1)^n for n >= 0.

Mathematica

LinearRecurrence[{1, 2}, {4, 1}, 28] (* Amiram Eldar, May 10 2021 *)

Crossrefs

Cf. A001045, A020714, A110286, A154879, A321421.

Cf. A014551, A156550, A084214.

Sequence in context: A158199 A091885 A069606 * A193580 A244761 A075150

Adjacent sequences: A344106 A344107 A344108 * A344110 A344111 A344112

Keyword

nonn,easy

Author

Paul Curtz, May 09 2021

Status

approved