A174239 a(n) = (3*n + 1 + (-1)^n*(n+3))/4.

1, 0, 3, 1, 5, 2, 7, 3, 9, 4, 11, 5, 13, 6, 15, 7, 17, 8, 19, 9, 21, 10, 23, 11, 25, 12, 27, 13, 29, 14, 31, 15, 33, 16, 35, 17, 37, 18, 39, 19, 41, 20, 43, 21, 45, 22, 47, 23, 49, 24, 51, 25, 53, 26, 55, 27, 57, 28, 59, 29, 61, 30, 63, 31, 65, 32, 67, 33, 69, 34, 71, 35, 73, 36, 75, 37, 77, 38, 79, 39, 81

Offset: 0

Author

Paul Curtz, Mar 13 2010

Keywords

• nonn
• easy

Comments

Obtained from A026741 by swapping pairs of consecutive entries.

The main diagonal of an array with this sequence in the top row and further rows defined by the first differences of their previous row is essentially 1 followed by 3*A045623(.):

1, 0, 3, 1, 5, 2, 7, 3, 9, 4, 11, 5, 13, 6, 15, 7, 17, 8, ...

-1, 3, -2, 4, -3, 5, -4, 6, -5, 7, -6, 8, -7, 9, -8, 10, -9, ...

4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, ...

-9, 11, -13, 15, -17, 19, -21, 23, -25, 27, -29, 31, ...

20, -24, 28, -32, 36, -40, 44, -48, 52, -56, 60, -64, ...

-44, 52, -60, 68, -76, 84, -92, 100, -108, 116, -124, 132, ...

96, -112, 128, -144, 160, -176, 192, -208, 224, -240, ...

Also, numerator of (Nimsum n+1)/2 = A004442(n)/2. - Wesley Ivan Hurt, Mar 21 2015

Links

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

Crossrefs

Cf. A004442.

Programs

Magma

[(3*n+1 +(-1)^n*(n+3))/4: n in [0..80]]; // Vincenzo Librandi, Feb 08 2011

Maple

A174239:=n->(3*n+1+(-1)^n*(n+3))/4: seq(A174239(n), n=0..100); # Wesley Ivan Hurt, Mar 21 2015

Mathematica

Table[(3 n + 1 + (-1)^n*(n + 3))/4, {n, 0, 100}] (* Wesley Ivan Hurt, Mar 21 2015 *)
LinearRecurrence[{0,2,0,-1},{1,0,3,1},90] (* Harvey P. Dale, Jul 16 2018 *)

Formula

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

a(n) = 2*a(n-2) - a(n-4).

a(2n+1) - 2*a(2n) = -A016789(n+1).

a(2n+2) - 2*a(2n+1) = 3.

G.f.: ( 1+x^2+x^3 ) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Feb 07 2011