A187541 a(4n+2) = 2n+1, otherwise a(n) = 4n.

0, 4, 1, 12, 16, 20, 3, 28, 32, 36, 5, 44, 48, 52, 7, 60, 64, 68, 9, 76, 80, 84, 11, 92, 96, 100, 13, 108, 112, 116, 15, 124, 128, 132, 17, 140, 144, 148, 19, 156, 160, 164, 21, 172, 176, 180, 23, 188, 192, 196, 25, 204, 208, 212, 27, 220, 224, 228, 29, 236, 240, 244, 31, 252

Offset: 0

Author

Paul Curtz, Mar 11 2011

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A008586, A010855, A060819, A061038.

Programs

Maple

A187541:=n->16*n/(11+7*(I^(2*n)-I^(-n)-I^n)): seq(A187541(n), n=0..100); # Wesley Ivan Hurt, Jul 05 2016

Mathematica

Table[16n/(11+7*(I^(2*n)-I^(-n)-I^n)), {n, 0, 80}] (* Wesley Ivan Hurt, Jul 05 2016 *)

Formula

a(n) = 2*a(n-4) - a(n-8) for n>7.

G.f.: x*(4+x+12*x^2+16*x^3+12*x^4+x^5+4*x^6)/(1-x^4)^2; a(n) = (n/8)*(32 -7*(1+(-1)^n)*(1-i^n)) where i=sqrt(-1). - Bruno Berselli, Mar 15 2011

From Paul Curtz, Mar 22 2011: (Start)

A060819(n)*a(n) = 0,4,1,36,16,100, = 0,4, followed by A061038(n+2).

a(n) = a(n-4) + period 4: repeat [16, 16, 2, 16]. Note that a(n) = 4*n/(period 4: repeat [1, 1, 8, 1]), Hence 16's = A010855. (End)

a(n) = 16*n/(11+7*(I^(2*n)-I^(-n)-I^n)). - Wesley Ivan Hurt, Jul 05 2016

Extensions

Edited by N. J. A. Sloane, Mar 15 2011