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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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 A325350

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

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Last modified August 11 06:25 EDT 2020. Contains 336422 sequences. (Running on oeis4.)