A392003 a(n) = (7*2^n - 9 + 5*(-1)^n) / 6.

0, 4, 7, 18, 35, 74, 147, 298, 595, 1194, 2387, 4778, 9555, 19114, 38227, 76458, 152915, 305834, 611667, 1223338, 2446675, 4893354, 9786707, 19573418, 39146835, 78293674, 156587347, 313174698, 626349395, 1252698794, 2505397587, 5010795178, 10021590355, 20043180714

Offset

1,2

Links

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..1000

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

Formula

Conjecture: a(2*n) = A266753(n).

From Stefano Spezia, Dec 27 2025: (Start)

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

E.g.f.: exp(-x)*(exp(x) - 1)^2*(7*exp(x) + 5)/6. (End)

Mathematica

a[n_] := (7*2^n - 9 + 5*(-1)^n)/6; Array[a, 35] (* Amiram Eldar, Dec 27 2025 *)
LinearRecurrence[{2, 1, -2}, {0, 4, 7}, 34] (* Hugo Pfoertner, Jan 01 2026 *)

Prog

(Python)
def A392003(n): return (7*2**n - 9 + 5*(-1)**n) // 6

Crossrefs

Cf. A266753, A390768.

Sequence in context: A285462 A146387 A219498 * A358078 A219754 A289975

Adjacent sequences: A392000 A392001 A392002 * A392004 A392005 A392006

Keyword

nonn,easy

Author

Karl-Heinz Hofmann, Dec 26 2025

Status

approved