A023438 -id:A023438 - cp's OEIS frontend

A172397 a(n) = a(n-1) + a(n-2) - a(n-3) - a(n-8), starting 1,1,2,2,3,3,4,4.

1, 1, 2, 2, 3, 3, 4, 4, 4, 3, 1, -2, -7, -13, -22, -32, -45, -58, -72, -83, -90, -88, -73, -39, 21, 113, 245, 420, 642, 905, 1200, 1502, 1776, 1965, 1994, 1763, 1150, 14, -1799, -4437, -8026, -12629, -18212, -24578, -31311, -37691, -42625, -44568, -41476

Offset: 0

Roger L. Bagula, Nov 20 2010

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,0,0,-1).

Cf. A023438.

a:=[1,1,2,2,3,3,4,4];; for n in [9..50] do a[n]:=a[n-1]+a[n-2]-a[n-3]-a[n-8]; od; a; # G. C. Greubel, Mar 01 2019

R:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x-x^2+x^3+x^8) )); // G. C. Greubel, Mar 01 2019

f[-6]=0; f[-5]=0; f[-4]=0; 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]-f[n-3]-f[n-8]; Table[f[n], {n, 0, 50}]
LinearRecurrence[{1,1,-1,0,0,0,0,-1},{1,1,2,2,3,3,4,4},50] (* Harvey P. Dale, Nov 20 2012 *)

my(x='x+O('x^50)); Vec(1/(1-x-x^2+x^3+x^8)) \\ G. C. Greubel, Mar 01 2019

(1/(1-x-x^2+x^3+x^8)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Mar 01 2019

G.f.: 1/(1 - x - x^2 + x^3 + x^8).

More terms from Harvey P. Dale, Nov 20 2012

A173199 a(n) = a(n-1)+a(n-2)-Floor(a(n-3)/2)-Floor(a(n-8)/2); initial terms are 0, 1, 1, 2, 3, 5, 7, 11.

Original entry on oeis.org

0, 1, 1, 2, 3, 5, 7, 11, 16, 24, 35, 50, 72, 103, 147, 209, 297, 421, 597, 845, 1196, 1692, 2393, 3383, 4782, 6759, 9552, 13498, 19073, 26949, 38077, 53799, 76011, 107393, 151729, 214368, 302865, 427895, 604538, 854102

Offset: 0

Roger L. Bagula, Nov 22 2010

nonn

A two wave dying rabbits type sequence with limiting ratio 1.41280984879641.

Cf. A023438 (dying rabbits).

I:=[0, 1, 1, 2, 3, 5, 7, 11]; [ n le 8 select I[n] else Self(n-1)+Self(n-2)-(Self(n-3) div 2)-(Self(n-8) div 2): n in [1..40] ];

f[-6] = 0; f[-5] = 0; f[-4] = 0; f[-3] = 0; f[-2] = 0; f[-1] = 0;
f[0] = 0; f[1] = 1;
f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 3]/2] - Floor[f[n -8]/2];
Table[f[n], {n, 0, 30}]

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.

Original entry on oeis.org

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

Roger L. Bagula, Nov 22 2010

nonn

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

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

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)).

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

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}]

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

cp's OEIS Frontend

A172397 a(n) = a(n-1) + a(n-2) - a(n-3) - a(n-8), starting 1,1,2,2,3,3,4,4.

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A173199 a(n) = a(n-1)+a(n-2)-Floor(a(n-3)/2)-Floor(a(n-8)/2); initial terms are 0, 1, 1, 2, 3, 5, 7, 11.

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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.

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