A193941 - OEIS

%I #26 Apr 01 2020 04:56:54

%S 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,

%T 370,475,610,784,1008,1296,1666,2141,2751,3535,4543,5839,7505,9646,

%U 12397,15932,20475,26314,33819,43465,55862,71794,92269,118583,152402

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

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

%H Vincenzo Librandi, <a href="/A193941/b193941.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1).

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

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

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

%t 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 *)

%o (PARI) Vec((1+x^3)/(1-x-x^6) + O(x^50)) \\ _Jinyuan Wang_, Apr 01 2020

%Y Cf. A005708.

%K nonn,easy

%O 0,4

%A _Johannes W. Meijer_, Aug 11 2011