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

0,3

Links

Table of n, a(n) for n=0..44.

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

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). - R. J. Mathar, Nov 25 2008

Example

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.

Mathematica

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

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 1, 0, 0, 1]^n*[0; 1; 2; 3])[1, 1] \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. A000045, A003269, A058278.

Sequence in context: A187067 A017831 A132289 * A154217 A361644 A185738

Adjacent sequences: A078464 A078465 A078466 * A078468 A078469 A078470

Keyword

nonn,easy,changed

Author

Arran Fernandez, Jan 02 2003

Status

approved