A173862 a(n) = A158772(n-1)/21.

1, 1, 1, 2, 2, 2, 4, 4, 4, 8, 8, 8, 16, 16, 16, 32, 32, 32, 64, 64, 64, 128, 128, 128, 256, 256, 256, 512, 512, 512, 1024, 1024, 1024, 2048, 2048, 2048, 4096, 4096, 4096, 8192, 8192, 8192, 16384, 16384, 16384, 32768, 32768, 32768, 65536, 65536, 65536, 131072, 131072

Offset: 1

Author

Paul Curtz, Nov 26 2010

Keywords

• nonn
• easy

Comments

Triplicated A000079. Powers of 2 repeated 3 times.

a(n) is the number of ways of partitioning the set of the first n distinct positive Fibonacci numbers into two subsets whose sums differ at most by 1. a(6) = 2: 1,2,5,8/3,13; 1,2,13/3,5,8. - Alois P. Heinz, Jun 16 2019

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2)

Crossrefs

Cf. A000045, A000079, A016116, A200672.

Programs

Mathematica

Flatten[Table[c=2^n;{c,c,c},{n,0,20}]] (* Harvey P. Dale, Jul 20 2012 *)
CoefficientList[Series[x*(1 + x + x^2)/(1 - 2*x^3), {x,0,50}], x] (* G. C. Greubel, Apr 30 2017 *)

PARI

a(n)=2^((n-1)\3) \\ Charles R Greathouse IV, Oct 03 2016

Formula

G.f. x*(1 + x + x^2)/(1 - 2*x^3). - R. J. Mathar, Nov 28 2011

Extensions

More terms from Harvey P. Dale, Jul 20 2012