|
| |
|
|
A131132
|
|
a(n) = a(n-1)+a(n-2)+1 if n is a multiple of 6, otherwise a(n) = a(n-1)+a(n-2).
|
|
2
| |
|
|
1, 1, 2, 3, 5, 8, 14, 22, 36, 58, 94, 152, 247, 399, 646, 1045, 1691, 2736, 4428, 7164, 11592, 18756, 30348, 49104, 79453, 128557, 208010, 336567, 544577, 881144, 1425722, 2306866, 3732588, 6039454, 9772042, 15811496, 25583539, 41395035, 66978574, 108373609
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Also: convolution of A000045 with the period-6 sequence (0,0,0,0,0,0, 1,...). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 30 2008
Sequences of the form s(0)=a, s(1)= b, s(n) =s(n-1)+s(n-2)+k if n mod m = p, else s(n)=s(n-1)+s(n-2) have a form s(n) = fibonacci(n-1)*a+fibonacci(n)*b+P(x)*k. a(n) is the P(x) sequence for m= 6. s(n)=fib(n)*a + fib(n-1)*b +a(n-6-p)*k [From Gary Detlefs (gdetlefs(At)aol.com) Dec 05 2010]
|
|
|
REFERENCES
| H. Matsui et al., Problem B-1035, Fibonacci Quarterly, Vol. 45, Number 2; 2007; p. 182.
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,0,0,0,1,-1,-1).
|
|
|
FORMULA
| O.g.f.: 1/((1-x^6)(1-x-x^2)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 30 2008
a(n) = ((-1)^n-1)/6 +A099837(n+3)/12 +A000045(n+4)/4 +A057079(n)/12. - R. J. Mathar, Dec 07 2010
a(n)= floor( A066983(n+4)/3) [From Gary Detlefs (gdetlefs(AT)aol.com) Dec 19 2010]
|
|
|
MAPLE
| A131132:=proc(n) option remember; local t1; if n <= 2 then RETURN(1); fi: if n mod 6 = 1 then t1:=1 else t1:=0; fi: procname(n-1)+procname(n-2)+t1; end; [seq(A131132(n), n=1..100)]; - N. J. A. Sloane (njas(AT)research.att.com), May 25 2008
|
|
|
MATHEMATICA
| a=0; b=0; lst={a, b}; Do[z=a+b+1; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z, {n, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 16 2010]
|
|
|
CROSSREFS
| Cf. A052952, A004695, A080239, A124502.
A066983
Sequence in context: A034416 A056366 A000046 * A004692 A094926 A078843
Adjacent sequences: A131129 A131130 A131131 * A131133 A131134 A131135
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 25 2008
|
|
|
EXTENSIONS
| Typo in Maple code corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 30 2008
More specific name from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 09 2009
|
| |
|
|
