A390561 Lower (1/5,1/2) midsequence of (2^n) and (5*n); see Comments.

0, 2, 5, 9, 13, 18, 27, 43, 71, 124, 229, 437, 849, 1670, 3311, 6591, 13147, 26256, 52473, 104905, 209765, 419482, 838915, 1677779, 3355503, 6710948, 13421837, 26843613, 53687161, 107374254, 214748439, 429496807, 858993539, 1717987000, 3435973921, 6871947761

Offset

0,2

Comments

Suppose that s = (s(n)) and t = (t(n)) are sequences of numbers and h > 0 and k > 0. The lower (h, k)-midsequence of s and t is floor(h*s + k*t); the upper (h, k)-midsequence of s and t is ceiling(h*s + k*t).

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (4,-6,6,-5,2).

Formula

a(n) = 4*a(n-1) - 6*a(n-2) + 6*a(n-3) - 5*a(n-4) + 2*a(n-5), with (a(0),...,a(4)) = (0, 2, 5, 9, 13).

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

Example

s = A000079 = (1, 2, 4, 8, 16, 32, 64, ...).
t = A000351 = (0, 5, 10, 15, 20, 25, 30, ...).
u(n) = (0, 2, 5, 9, 13, 18, 27, 43, ...).
v(n) = (1, 3, 6, 10, 14, 19, 28, 44, ...).

Mathematica

s[n_] := 2^n ; t[n_] := 5*n; h = 1/5; k = 1/2;
u[n_] := Floor[h*s[n] + k*t[n]];
v[n_] := Ceiling[h*s[n] + k*t[n]];
Table[u[n], {n, 0, 60}]  (* A390561 *)
Table[v[n], {n, 0, 60}]  (* A390562 *)
(* Also *)
LinearRecurrence[{4, -6, 6, -5, 2}, {0, 2, 5, 9, 13}, 30]

Crossrefs

Cf. A000079, A008587, A389123, A390562.

Sequence in context: A130235 A267531 A219647 * A129726 A122489 A120615

Adjacent sequences: A390558 A390559 A390560 * A390562 A390563 A390564

Keyword

nonn,easy

Author

Clark Kimberling, Nov 11 2025

Status

approved