A171997 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2) - floor(a(n-5)/2); initial terms are 1, 1, 2, 3, 4.

1, 1, 2, 3, 4, 6, 8, 10, 13, 16, 20, 24, 29, 35, 42, 50, 59, 70, 83, 97, 114, 134, 156, 182, 212, 246, 285, 330, 382, 441, 509, 588, 678, 781, 900, 1037, 1193, 1373, 1580, 1817, 2089, 2402, 2761, 3172, 3645, 4187, 4809, 5523, 6342, 7282, 8360

Offset

1,3

Comments

lim_{n -> infinity} a(n+1)/a(n) = 1.14710876512065387719410850648860644150605499412513....

a(n) = A062435(n+2) for n < 15.

Links

Table of n, a(n) for n=1..51.

Mathematica

f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 2]/2] - Floor[f[n - 5]/2]
Table[f[n], {n, 0, 50}]

Prog

(Magma) I:=[1, 1, 2, 3, 4]; [n le 5 select I[n] else Self(n-1) + Self(n-2) - Floor(Self(n-2)/2) - Floor(Self(n-5)/2): n in [1..60]]; // Vincenzo Librandi, Jun 24 2015

Crossrefs

Cf. A062435 (integer part of log(n!)^log(log(1 + n))), A023434 (a(n)=a(n-1)+a(n-2)-a(n-4)), A023435 (a(n)=a(n-1)+a(n-2)-a(n-5)), A023436 (a(n)=a(n-1)+a(n-2)-a(n-6)), A023437 (a(n)=a(n-1)+a(n-2)-a(n-7)), A023438 (a(n)=a(n-1)+a(n-2)-a(n-8)), A023439 (a(n)=a(n-1)+a(n-2)-a(n-9)), A023440 (a(n)=a(n-1)+a(n-2)+a(n-10)), A023441 (a(n)=a(n-1)+a(n-2)-a(n-11)), A023442 (a(n)=a(n-1)+a(n-2)-a(n-12)), A000044 (a(n)=a(n-1)+a(n-2)-a(n-13)), A173199 (a(n)=a(n-1)+a(n-2)-floor(a(n-3)/2)-floor(a(n-8)/2)).

Sequence in context: A008669 A055104 A062435 * A020702 A067996 A074715

Adjacent sequences: A171994 A171995 A171996 * A171998 A171999 A172000

Keyword

nonn

Author

Roger L. Bagula, Nov 22 2010

Extensions

Offset changed from 0 to 1 by Klaus Brockhaus, Nov 29 2010

Status

approved