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

Author

N. J. A. Sloane, Feb 13 2019

Keywords

• nonn

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

Crossrefs

Cf. A191386.

Programs

Mathematica

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

PARI

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

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.