A115639 First column of divide-and-conquer triangle A115636.

1, 1, 4, 4, 4, 4, 16, 16, 16, 16, 16, 16, 16, 16, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256, 256

Offset: 0

Author

Paul Barry, Jan 27 2006

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000523, A115636.

Programs

Magma

[4^(Ilog2(n+2) -1) : n in [0..80] ]; // G. C. Greubel, Nov 23 2021

Mathematica

4^(Floor[Log[2, Range[0, 80] +2]] -1) (* G. C. Greubel, Nov 23 2021 *)

Sage

[4^(floor(log(n+2, 2)) -1) for n in (0..80)] # G. C. Greubel, Nov 23 2021

Formula

G.f.: (1/(1-x))*( 1/4 + (3/4)*Sum_{k>=1} 4^(k-1)*x^(2^k-2) ).

a(n) = 4^(floor(log_2(n+2)) - 1). - G. C. Greubel, Nov 23 2021