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A273692 a(n) is the denominator of 2*O(n+1) - O(n+2) where O(n) = n/2^n, the n-th Oresme number. 1
2, 8, 2, 32, 32, 128, 64, 512, 512, 2048, 128, 8192, 8192, 32768, 16384, 131072, 131072, 524288, 131072, 2097152, 2097152, 8388608, 4194304, 33554432, 33554432, 134217728, 16777216, 536870912, 536870912, 2147483648, 1073741824, 8589934592, 8589934592, 34359738368 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

O(n) is the Horadam notation.

O(n) or Oresme(n) = n/2^n = 0, 1/2, 1/2, 3/8, 1/4, ... . The positive Oresme numbers are O(n+1) = A000265(n+1)/A075101(n+1). See A209308. Consider Oco(n) = 2*O(n+1) - O(n+2) = 1/2, 5/8, 1/2, 11/32, 7/32, ... = A075677(n+1)/a(n). (See Coll(n) in A209308).

Oco(n) = 1/2, 5/8, 1/2, 11/32, 7/32, 17/128, 5/64, 23/512, 13/512, 29/2048, 1/128, 35/8192, 19/8192, ... . Compare to (2+3*n)/2^(n+2).

Differences table of Oco(n):

1/2,       5/8,   1/2,  11/32,    7/32, 17/128, 5/64, ...

1/8,      -1/8, -5/32,   -1/8, -11/128, -7/128, ...

-1/4,    -1/32,  1/32,  5/128,    1/32, ...

7/32,     1/16, 1/128, -1/128, ...

-5/32,  -7/128, -1/64, ...

13/128,  5/128, ...

-1/16, ... .

First column: Io(n) = 1/2 followed by (-1)^n* A067745(n)/(8, 4, 32, 32, ...).

1) Alternated Oco(2n) + Io(2n) and Oco(2n+1) - Io(2n+1) gives 2^n.

2) Alternated Oco(2n) - Io(2n) and Oco(2n+1) + Io(2n+1) gives 3*O(n)/2.

   (1/2-1/2=0, 5/8+1/8=3/4, 1/2+1/4=3/4, 11/32+7/32=9/16, ...)

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..3320

A. F. Horadam, Oresme numbers, Fib. Quart., 12 (1974), 267-271.

FORMULA

a(n) = denominator of (2+3*n)/2^(n+2).

a(2n+1) = 8*4^n.

a(2n+2) = a(2n+1)/(4, 1, 2, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, ... , shifted A006519?).

PROG

(PARI) Or(n) = n/2^n;

a(n) = denominator(2*Or(n+1) - Or(n+2)); \\ Michel Marcus, May 28 2016

CROSSREFS

Cf. A000079, A000265, A000302, A004171 (main diagonal), A006519, A016789, A067745, A075101, A075677, A209308.

Sequence in context: A245995 A085192 A320972 * A006085 A021357 A214072

Adjacent sequences:  A273689 A273690 A273691 * A273693 A273694 A273695

KEYWORD

nonn,frac

AUTHOR

Paul Curtz, May 28 2016

EXTENSIONS

More terms from Michel Marcus, May 28 2016

STATUS

approved

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Last modified January 29 10:34 EST 2020. Contains 331337 sequences. (Running on oeis4.)