A343176 a(0)=3; for n > 0, a(n) = 2^(2*n) + 3*2^(n-1) + 1.

3, 8, 23, 77, 281, 1073, 4193, 16577, 65921, 262913, 1050113, 4197377, 16783361, 67121153, 268460033, 1073790977, 4295065601, 17180065793, 68719869953, 274878693377, 1099513200641, 4398049656833, 17592192335873, 70368756760577, 281475001876481, 1125899957174273, 4503599728033793

Offset

0,1

Comments

A bisection of A257418. Apart from first term, same as A036562.

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Formula

From Chai Wah Wu, Apr 26 2021: (Start)

a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n > 3.

G.f.: -(4*x - 3)*(x^2 + 3*x - 1)/((x - 1)*(2*x - 1)*(4*x - 1)). (End)

Mathematica

A343176[n_] := Floor[4^n + 3*2^(n-1) + 1]; Array[A343176, 30, 0] (* Paolo Xausa, Jul 02 2026 *)

Prog

(PARI) a(n) = if(n==0, 3, 1<<(2*n) + 3<<(n-1) + 1); \\ Bruce Nye, Jul 03 2026

Crossrefs

Cf. A257418, A036562, A343175.

Sequence in context: A024716 A189359 A125782 * A307875 A321730 A047143

Adjacent sequences: A343173 A343174 A343175 * A343177 A343178 A343179

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 26 2021

Extensions

a(17)-a(26) from Martin Ehrenstein, Apr 26 2021

Status

approved