A132314 a(n) = n*2^floor((n+1)/2).
0, 2, 4, 12, 16, 40, 48, 112, 128, 288, 320, 704, 768, 1664, 1792, 3840, 4096, 8704, 9216, 19456, 20480, 43008, 45056, 94208, 98304, 204800, 212992, 442368, 458752, 950272, 983040, 2031616, 2097152, 4325376, 4456448, 9175040, 9437184, 19398656, 19922944, 40894464
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Simon Plouffe, Illustration.
- Index entries for linear recurrences with constant coefficients, signature (0,4,0,-4).
Programs
-
Maple
seq(n*2^(floor((n+1)/2)),n=0..120);
-
Mathematica
LinearRecurrence[{0,4,0,-4}, {0, 2, 4, 12}, 50] (* G. C. Greubel, May 30 2016 *)
Formula
a(n) = 2*A093968(n).
From Chai Wah Wu, May 30 2016: (Start)
a(n) = 4*a(n-2) - 4*a(n-4) for n > 3.
G.f.: 2*x*(2*x^2 + 2*x + 1)/(2*x^2 - 1)^2. (End)
E.g.f.: x*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)). - G. C. Greubel, May 30 2016
Sum_{n>=1} 1/a(n) = log(2)/2 + log(1+sqrt(2))/sqrt(2). - Amiram Eldar, Feb 13 2023