A193941 G.f.: (1+x^3)/(1-x-x^6).

1, 1, 1, 2, 2, 2, 3, 4, 5, 7, 9, 11, 14, 18, 23, 30, 39, 50, 64, 82, 105, 135, 174, 224, 288, 370, 475, 610, 784, 1008, 1296, 1666, 2141, 2751, 3535, 4543, 5839, 7505, 9646, 12397, 15932, 20475, 26314, 33819, 43465, 55862, 71794, 92269, 118583, 152402

Offset: 0

Author

Johannes W. Meijer, Aug 11 2011

Keywords

• nonn
• easy

Comments

The Ca1 sums, see A180662, of triangle A065941 equal the terms of this sequence.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1).

Crossrefs

Cf. A005708.

Programs

Maple

A193941 := proc(n): coeftayl((1+x^3)/(1-x-x^6),x=0,n) end: seq(A193941(n),n=0..49);

Mathematica

CoefficientList[Series[(1+x^3)/(1-x-x^6),{x,0,50}],x] (* or *) LinearRecurrence[{1,0,0,0,0,1},{1,1,1,2,2,2},50] (* Harvey P. Dale, Apr 25 2014 *)

PARI

Vec((1+x^3)/(1-x-x^6) + O(x^50)) \\ Jinyuan Wang, Apr 01 2020

Formula

G.f.: (1+x)*(1-x+x^2)/(1-x-x^6).

a(n) = A005708(n) + A005708(n-3).