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A141310 The odd numbers interlaced with the constant-2 sequence. 1
1, 2, 3, 2, 5, 2, 7, 2, 9, 2, 11, 2, 13, 2, 15, 2, 17, 2, 19, 2, 21, 2, 23, 2, 25, 2, 27, 2, 29, 2, 31, 2, 33, 2, 35, 2, 37, 2, 39, 2, 41, 2, 43, 2, 45, 1, 47, 2, 49, 2, 51, 2, 53, 2, 55, 2, 57, 2, 59, 2, 61, 2, 63, 2, 65 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Similarly, the principle of interlacing a sequence and its first differences leads from A000012 and its differences A000004 to A059841, or from A140811 and its first differences A017593 to a sequence -1, 6, 5, 18,...

If n is even then a(n) = n + 1 ; otherwise a(n) = 2. - Wesley Ivan Hurt, Jun 05 2013

Denominators of floor((n+1)/2) / (n+1), n > 0. [Wesley Ivan Hurt, Jun 14 2013]

LINKS

Table of n, a(n) for n=0..64.

FORMULA

a(2n) = A005408(n). a(2n+1) = 2.

First differences: a(n+1) - a(n) = (-1)^(n+1)*A109613(n-1), n > 0.

b(2n) = -A008586(n), and b(2n+1) = A060747(n), where b(n) = a(n+1) - 2*a(n).

a(n) = 2*a(n-2) - a(n-4). G.f.: (1+2*x+x^2-2*x^3)/((x-1)^2*(1+x)^2). - R. J. Mathar, Feb 23 2009

Contribution from Wesley Ivan Hurt, Jun 05 2013 (Start):

a(n) = n + 1 - (n - 1)*(n mod 2).

a(n) = (n + 1) * (n - floor((n+1)/2))! / floor((n+1)/2)!.

a(n) = A000142(n+1) / A211374(n+1). (end)

MAPLE

a(n):=n->n+1-(n-1)*(n mod 2); seq(a(k), k=1..100); # Wesley Ivan Hurt, Jun 05 2013

MATHEMATICA

Flatten[Table[{2n - 1, 2}, {n, 40}]] (* Alonso del Arte, Jun 15 2013 *)

Riffle[Range[1, 79, 2], 2] (* Requires version 6.0+. - Alonso del Arte, Jun 14 2013 *)

CROSSREFS

Cf. A000004, A000012, A000142, A005408, A008586, A017593, A059841, A060747, A109613, A140811, A141310, A211374.

Sequence in context: A088444 A108077 A248737 * A007389 A007388 A057815

Adjacent sequences:  A141307 A141308 A141309 * A141311 A141312 A141313

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Aug 02 2008

EXTENSIONS

Edited by R. J. Mathar, Feb 23 2009

STATUS

approved

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Last modified December 2 19:13 EST 2016. Contains 278683 sequences.