A105452 a(n) = numerator of (7*n - 1)/3.

2, 13, 20, 9, 34, 41, 16, 55, 62, 23, 76, 83, 30, 97, 104, 37, 118, 125, 44, 139, 146, 51, 160, 167, 58, 181, 188, 65, 202, 209, 72, 223, 230, 79, 244, 251, 86, 265, 272, 93, 286, 293, 100, 307, 314, 107, 328, 335, 114, 349, 356, 121, 370, 377, 128, 391, 398, 135, 412, 419

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

Formula

a(3*n+1) = 7*n+2 = A017005(n), a(3*n+2) = 2*n+13, a(3*n+3) = 21*n+20.

From Chai Wah Wu, Sep 24 2020: (Start)

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

G.f.: x*(x^5 + 8*x^4 + 5*x^3 + 20*x^2 + 13*x + 2)/(x^6 - 2*x^3 + 1). (End)

E.g.f.: (9 + 7*exp(x)*(7*x - 1) + exp(-x/2)*(2*sqrt(3)*sin(sqrt(3)*x/2) - 2*(1 + 14*x)*cos(sqrt(3)*x/2)))/9. - Stefano Spezia, Jun 04 2026

Mathematica

Numerator[(7*Range[60] - 1)/3] (* Paolo Xausa, Jun 04 2026 *)

Crossrefs

Cf. A017005.

Sequence in context: A121181 A007355 A339611 * A219278 A099419 A061871

Adjacent sequences: A105449 A105450 A105451 * A105453 A105454 A105455

Keyword

nonn,frac,easy,changed

Author

Zak Seidov, May 02 2005

Extensions

More terms from Paolo Xausa, Jun 04 2026

Status

approved