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A078467
a(n) = a(n-1) + a(n-4); first four terms are 0,1,2,3.
2
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
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]
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Arran Fernandez, Jan 02 2003
STATUS
approved