A127944 Partial sums of A093049.

0, 0, 0, 2, 3, 7, 11, 17, 21, 29, 37, 47, 56, 68, 80, 94, 105, 121, 137, 155, 172, 192, 212, 234, 254, 278, 302, 328, 353, 381, 409, 439, 465, 497, 529, 563, 596, 632, 668, 706, 742, 782, 822, 864, 905, 949, 993, 1039, 1082, 1130, 1178, 1228, 1277

Offset: 0

Author

Paul Barry, Feb 08 2007

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Programs

Magma

[Floor(Log(2,(2^Binomial(n+1,2) / Denominator(Binomial(2*n,n) / 4^n)))): n in [0..80]]; // Vincenzo Librandi, May 02 2018

Mathematica

Table[Log2[2^Binomial[n + 1, 2]/Denominator[Binomial[2 n, n]/4^n]], {n, 0, 100}] (* G. C. Greubel, May 01 2018 *)
Accumulate[Join[{0},Table[n-1-IntegerExponent[n,2],{n,80}]]] (* Harvey P. Dale, Nov 15 2022 *)

Formula

a(n) = log_2(2^C(n+1,2)/denominator(C(2n,n)/4^n)).

a(n) = A000217(n) - A005187(n).

a(n) = log_2(A127943(n)).