A141310 The odd numbers interlaced with the constant-2 sequence.

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, 2, 47, 2, 49, 2, 51, 2, 53, 2, 55, 2, 57, 2, 59, 2, 61, 2, 63, 2, 65, 2, 67, 2, 69, 2, 71, 2, 73, 2, 75, 2, 77, 2, 79, 2, 81, 2, 83, 2, 85, 2, 87, 2, 89, 2, 91, 2, 93, 2, 95, 2, 97

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

a(n) is also the number of minimum total dominating sets in the (n+1)-gear graph for n>1. - Eric W. Weisstein, Apr 11 2018

a(n) is also the number of minimum total dominating sets in the (n+1)-sun graph for n>1. - Eric W. Weisstein, Sep 09 2021

Denominators of Cesàro means sequence of A114112, corresponding numerators are in A354008. - Bernard Schott, May 14 2022

Also, denominators of Cesàro means sequence of A237420, corresponding numerators are in A354280. - Bernard Schott, May 22 2022

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Eric Weisstein's World of Mathematics, Gear Graph

Eric Weisstein's World of Mathematics, Sun Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

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). - R. J. Mathar, Feb 23 2009

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

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[{2 n - 1, 2}, {n, 40}]] (* Alonso del Arte, Jun 15 2013 *)
Riffle[Range[1, 79, 2], 2] (* Alonso del Arte, Jun 14 2013 *)
Table[((-1)^n (n - 1) + n + 3)/2, {n, 0, 20}] (* Eric W. Weisstein, Apr 11 2018 *)
Table[Floor[(n + 1)/2]/(n + 1), {n, 0, 20}] // Denominator (* Eric W. Weisstein, Apr 11 2018 *)
LinearRecurrence[{0, 2, 0, -1}, {2, 3, 2, 5}, {0, 20}] (* Eric W. Weisstein, Apr 11 2018 *)
CoefficientList[Series[(1 + 2 x + x^2 - 2 x^3)/(-1 + x^2)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Apr 11 2018 *)

Prog

(PARI) A141310(n) = if(n%2, 2, 1+n); \\ (for offset=0 version) - Antti Karttunen, Oct 02 2018
(PARI) A141310off1(n) = if(n%2, n, 2); \\ (for offset=1 version) - Antti Karttunen, Oct 02 2018
(Python)
def A141310(n): return 2 if n % 2 else n + 1 # Chai Wah Wu, May 24 2022

Crossrefs

Cf. A000004, A000012, A000142, A005408, A008586, A017593, A059841, A060747, A109613, A140811, A211374, A319702 (rgs-transform).

Cf. A114112, A354008.

Cf. A237420, A354280.

Sequence in context: A088444 A108077 A248737 * A007389 A007388 A348846

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

Term a(45) corrected, and more terms added by Antti Karttunen, Oct 02 2018

Status

approved