A323988 a(n) = 2^(n - 1) + binomial(n, floor(n/2))*(n + 1)/2.

1, 2, 5, 10, 23, 46, 102, 204, 443, 886, 1898, 3796, 8054, 16108, 33932, 67864, 142163, 284326, 592962, 1185924, 2464226, 4928452, 10209620, 20419240, 42190558, 84381116, 173962532, 347925064, 715908428, 1431816856, 2941192472, 5882384944, 12065310083, 24130620166

Offset

0,2

Comments

This sequence was obtained by omitting the two initial zeros from A191386, which has a more complicated definition. The simple formula defining this sequence was found by Dan Velleman and Stan Wagon. See A191386 for further information, including references.

Links

Winston de Greef, Table of n, a(n) for n = 0..3300

Formula

G.f. = (1+s)/(2*s*(1-2*x), where s = sqrt(1-4*x^2).

a(0) = 1, a(1) = 2, a(2) = 5; thereafter (8*n+16)*a(n) + (-4*n-8)*a(n+1) + (-2*n-6)*a(n+2) + (n+3)*a(n+3) = 0.

Mathematica

A323988[n_]:=2^(n-1)+Binomial[n, Floor[n/2]](n+1)/2; Array[A323988, 50, 0] (* Paolo Xausa, Nov 17 2023 *)

Prog

(PARI) a(n) = 2^(n-1) + binomial(n, n\2)*(n+1)/2 \\ Winston de Greef, Sep 17 2023

Crossrefs

Cf. A191386.

Sequence in context: A174542 A007182 A191386 * A026677 A109165 A018344

Adjacent sequences: A323985 A323986 A323987 * A323989 A323990 A323991

Keyword

nonn

Author

N. J. A. Sloane, Feb 13 2019

Status

approved