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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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The plot has a potential-like dip in it.

All the roots of the characteristic polynomial are complex, so the sequence is quite chaotic.

I've been feeding some desert cottontail rabbits in my back yard. Yesterday I had to bury one. I estimated it was between 4 and 6 generations old: died of old age and winter.

I tried those as Fibonacci sequences and found the dying rabbit sequences. This sequence was my idea to get two waves of dying in the rabbits: early and late.

LINKS

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).

FORMULA

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

MATHEMATICA

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 *)

PROG

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

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

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

(GAP) 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

CROSSREFS

Cf. A023438.

Sequence in context: A079730 A035486 A282347 * A237815 A238701 A238134

Adjacent sequences:  A172394 A172395 A172396 * A172398 A172399 A172400

KEYWORD

sign

AUTHOR

Roger L. Bagula, Nov 20 2010

EXTENSIONS

More terms from Harvey P. Dale, Nov 20 2012

STATUS

approved

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Last modified April 6 11:51 EDT 2020. Contains 333273 sequences. (Running on oeis4.)