OFFSET
0,4
REFERENCES
C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 95.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
A. F. Horadam, Oresme numbers, Fib. Quart., 12 (1974), 267-271.
FORMULA
a(n) = numerator(2-(n+2)/2^n).
If n+2=2^k*m with m odd, then a(n) = 2^(n+1-k) - m.
Numerators of coefficients in expansion of 2*x / ((1 - x) * (2 - x)^2). - Ilya Gutkovskiy, Aug 04 2023
MAPLE
seq(numer(2-(n+2)/2^n), n=0..50); # Ridouane Oudra, Jul 16 2023
MATHEMATICA
a[n_] := Module[{k, m}, For[k = 0; m = n + 2, EvenQ[m], k++, m/=2]; 2^(n + 1 - k) - m]
Table[Numerator[Sum[i/2^i, {i, n}]], {n, 40}] (* Alonso del Arte, Aug 12 2012 *)
PROG
(PARI) concat(0, vector(100, n, numerator(sum(i=1, n, i/2^i)))) \\ Colin Barker, Nov 09 2014
(PARI) a(n) = numerator(2-(n+2)/2^n); \\ Joerg Arndt, Jul 17 2023
(Magma) [0] cat [Numerator(&+[i/2^i: i in [1..n]]): n in [1..40]]; // Vincenzo Librandi, Nov 09 2014
CROSSREFS
KEYWORD
nonn,easy,frac
AUTHOR
STATUS
approved