|
%I #14 Jun 13 2015 00:50:49
%S 0,1,2,3,3,4,6,9,12,16,22,31,43,59,81,112,155,214,295,407,562,776,
%T 1071,1478,2040,2816,3887,5365,7405,10221,14108,19473,26878,37099,
%U 51207,70680,97558,134657,185864,256544,354102,488759,674623,931167,1285269
%N a(n) = a(n-1) + a(n-4); first four terms are 0,1,2,3.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1).
%F a(n) = a(n-1) + a(n-4); a(0)=0, a(1)=1, a(2)=2, a(3)=3
%F a(n+1)=sum{k=0..n, binomial(n-k, floor(k/3))} - _Paul Barry_, Jul 06 2004
%F G.f.: x(1+x+x^2)/(1-x-x^4). a(n)=A003269(n)+A003269(n-1)+A003269(n-2). [From _R. J. Mathar_, Nov 25 2008]
%e The sequence begins 0,1,2,3. a(5) = a(5-1) + a(5-4) = a(4)+a(1)= 3+0 =3. a(6) = a(6-1) + a(6-4) = a(5) + a(2) = 3+1 = 4.
%t LinearRecurrence[{1,0,0,1},{0,1,2,3},50] (* _Harvey P. Dale_, Oct 08 2012 *)
%Y Cf. A000045, A003269, A058278.
%K nonn
%O 0,3
%A _Arran Fernandez_, Jan 02 2003
|
