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

Author

Roger L. Bagula, Nov 22 2010

Keywords

• nonn

Comments

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

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

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)).

Programs

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

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}]

Extensions

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