A370627 a(n) = 2^(n - 1)*((-1)^(n + 1) + 7*2^n)/3 = 2^(n - 1)*A062092(n).

1, 5, 18, 76, 296, 1200, 4768, 19136, 76416, 305920, 1223168, 4893696, 19572736, 78295040, 313171968, 1252704256, 5010784256, 20043202560, 80172679168, 320690978816, 1282763390976, 5131054612480, 20524216352768, 82096869605376, 328387470032896, 1313549896908800, 5254199554080768

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (2,8).

Formula

Binomial transform of A133125.

G.f.: (1 + 3*x)/(1 - 2*x - 8*x^2).

E.g.f.: (1/3)*exp(x)*(3*exp(3*x) + sinh(3*x)).

a(n) = 2*a(n-1) + 8*a(n-2), for n > 1.

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

a(n) = (a(n+2) - 2*a(n+1))/8.

From Thomas Scheuerle, Jul 03 2024: (Start)

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

a(n) = A003683(n) + 4^n.

a(n) = A255470(2^n - 1) - A255470(2^(n-1) - 1) = A255471(n) - A255471(n-1), for n > 0. (End)

Binomial transform: A108982.

Mathematica

LinearRecurrence[{2, 8}, {1, 5}, 27] (* Amiram Eldar, Jul 03 2024 *)

Prog

(PARI) a(n) = 2^(n-1)*((-1)^(n+1) + 7*2^n)/3 \\ Thomas Scheuerle, Jul 03 2024

Crossrefs

Cf. A003683, A122803, A133125, A255470, A255471.

Cf. A108982, A062092.

Sequence in context: A296123 A375705 A242054 * A027134 A227451 A017960

Adjacent sequences: A370624 A370625 A370626 * A370628 A370629 A370630

Keyword

nonn,easy

Author

Paul Curtz, Jul 03 2024

Status

approved