A059029 a(n) = n if n is even, 2*n + 1 if n is odd.

0, 3, 2, 7, 4, 11, 6, 15, 8, 19, 10, 23, 12, 27, 14, 31, 16, 35, 18, 39, 20, 43, 22, 47, 24, 51, 26, 55, 28, 59, 30, 63, 32, 67, 34, 71, 36, 75, 38, 79, 40, 83, 42, 87, 44, 91, 46, 95, 48, 99, 50, 103, 52, 107, 54, 111, 56, 115, 58, 119, 60, 123, 62, 127, 64, 131, 66, 135

Offset: 0

Author

Asher Auel, Dec 15 2000

Keywords

• nonn
• easy

Comments

a(n-1) = n^k - 1 mod 2*n, n >= 1, for any k >= 2, also for k = n. - Wolfdieter Lang, Dec 21 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for two-way infinite sequences
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A059026, A059030, A059031.

a(n) = A022998(n+1) - 1 = A043547(n+3) - 3. Partial sums in A032438.

Programs

Magma

[n+((n+1)/2)*(1-(-1)^n): n in [0..70]]; // Vincenzo Librandi, Aug 14 2011

Maple

B := (n,m) -> lcm(n,m)/n + lcm(n,m)/m - 1: seq(B(m+2,m),m=1..90);

Mathematica

Table[n +(n+1)*(1-(-1)^n)/2, {n,0,70}] (* G. C. Greubel, Nov 08 2018 *)
Table[If[EvenQ[n],n,2n+1],{n,0,70}] (* or *) LinearRecurrence[{0,2,0,-1},{0,3,2,7},70] (* Harvey P. Dale, Jul 23 2025 *)

PARI

a(n)=if(n%2,2*n+1,n)

Formula

G.f.: x*(x^2 + 2*x + 3)/(1 - x^2)^2. - Ralf Stephan, Jun 10 2003

Third main diagonal of A059026: a(n) = B(n+2, n) = lcm(n+2, n)/(n+2) + lcm(n+2, n)/n - 1 for all n >= 1.

a(2*n) + a(2*n+1) = A016945(n). - Paul Curtz, Aug 29 2008

E.g.f.: 2*x*cosh(x) + (1 + x)*sinh(x). - Franck Maminirina Ramaharo, Nov 08 2018

Extensions

New description from Ralf Stephan, Jun 10 2003