A188146 Three interleaved 1st-order polynomials: a(3*n) = 1+4*n, a(1+3*n) = 3+4*n, a(2+3*n) = 1+n.

1, 3, 1, 5, 7, 2, 9, 11, 3, 13, 15, 4, 17, 19, 5, 21, 23, 6, 25, 27, 7, 29, 31, 8, 33, 35, 9, 37, 39, 10, 41, 43, 11, 45, 47, 12, 49, 51, 13, 53, 55, 14, 57, 59, 15, 61, 63, 16, 65, 67, 17, 69, 71, 18, 73, 75, 19, 77, 79, 20, 81, 83, 21, 85, 87, 22, 89, 91, 23, 93, 95, 24, 97, 99, 25, 101, 103, 26, 105, 107, 27, 109, 111

Offset: 0

Author

Paul Curtz, Mar 22 2011

Keywords

• nonn
• less
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Programs

Mathematica

CoefficientList[Series[(1+3x+x^2+3x^3+x^4)/((x-1)^2(1+x+x^2)^2), {x,0,85}],x] (* Harvey P. Dale, Apr 09 2011 *)

PARI

Vec((1+3*x+x^2+3*x^3+x^4 ) / ((x-1)^2*(1+x+x^2)^2) + O(x^100)) \\ Colin Barker, Mar 06 2017

Formula

a(n)= 2*a(n-3) - a(n-6).

a(3*n) + a(1+3*n) + a(2+3*n) = 5+9*n.

a(n) = n + 1 - (-1)^n*A099254(n-1). - R. J. Mathar, Mar 31 2011

G.f.: ( 1+3*x+x^2+3*x^3+x^4 ) / ( (x-1)^2*(1+x+x^2)^2 ). - R. J. Mathar, Mar 31 2011

a(n) = (9*(n+1) + sqrt(3)*(3*n+4)*sin((2*Pi*n)/3) + 3*n*cos((2*Pi*n)/3)) / 9. - Colin Barker, Mar 06 2017