A078467 a(n) = a(n-1) + a(n-4); first four terms are 0,1,2,3.

0, 1, 2, 3, 3, 4, 6, 9, 12, 16, 22, 31, 43, 59, 81, 112, 155, 214, 295, 407, 562, 776, 1071, 1478, 2040, 2816, 3887, 5365, 7405, 10221, 14108, 19473, 26878, 37099, 51207, 70680, 97558, 134657, 185864, 256544, 354102, 488759, 674623, 931167, 1285269

Offset: 0

Author

Arran Fernandez, Jan 02 2003

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A000045, A003269, A058278.

Programs

Mathematica

LinearRecurrence[{1,0,0,1},{0,1,2,3},50] (* Harvey P. Dale, Oct 08 2012 *)

Formula

a(n) = a(n-1) + a(n-4); a(0)=0, a(1)=1, a(2)=2, a(3)=3

a(n+1)=sum{k=0..n, binomial(n-k, floor(k/3))} - Paul Barry, Jul 06 2004

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]