A013982 -id:A013982 - cp's OEIS frontend

A109544 Expansion of (1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5).

1, 1, 1, 1, 1, 4, 4, 7, 10, 16, 25, 37, 58, 88, 136, 208, 319, 490, 751, 1153, 1768, 2713, 4162, 6385, 9796, 15028, 23056, 35371, 54265, 83251, 127720, 195943, 300607, 461179, 707521, 1085449, 1665250, 2554756, 3919399, 6012976, 9224854, 14152381

Offset: 0

Roger L. Bagula, Jun 20 2005

Peter Borwein and Kevin G. Hare, Some Computations on Pisot and Salem Numbers, CARMA Preprint, 2000, p.7, Table 1.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,1).

Cf. A013982.

Cf. A107479, A107480, A109538, A109543, A114749, A125950, A130844, A143335, A147851.

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x-x^3-2*x^4)/(1-x^2-x^3-x^4-x^5))); // G. C. Greubel, Nov 03 2018

LinearRecurrence[{0, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, 50]
CoefficientList[Series[(1+x-x^3-2x^4)/(1-x^2-x^3-x^4-x^5),{x,0,50}],x] (* Harvey P. Dale, Oct 24 2021 *)

makelist(ratcoef(taylor((1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5), x, 0, n), x, n), n, 0, 50); /* Franck Maminirina Ramaharo, Oct 31 2018 */

x='x+O('x^50); Vec((1+x-x^3-2*x^4)/(1-x^2-x^3-x^4-x^5)) \\ G. C. Greubel, Nov 03 2018

a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5).

A072465 A Fibonacci-like model in which each pair of rabbits dies after the birth of their 4th litter: a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5).

Original entry on oeis.org

1, 1, 1, 2, 3, 5, 7, 11, 17, 26, 40, 61, 94, 144, 221, 339, 520, 798, 1224, 1878, 2881, 4420, 6781, 10403, 15960, 24485, 37564, 57629, 88412, 135638, 208090, 319243, 489769, 751383, 1152740, 1768485, 2713135, 4162377, 6385743, 9796737

Offset: 0

Leonardo Fonseca (fonleo(AT)fisica.ufmg.br), Jun 19 2002

Lim_{n->infinity} a(n+1)/a(n) = 1.534157744914.... is the root of x^5 = x^3 + x^2 + x + 1. - Benoit Cloitre, Jun 22 2002

A pair of rabbits born in month n begins to procreate in month n + 2, continues to procreate until month n + 5, and dies at the end of this month (each pair therefore gives birth to 5-2+1 = 4 pairs); the first pair is born in month 1. - Robert FERREOL, Oct 05 2017

N. T. Gridgeman, A New Look at Fibonacci Generalization, Fibonacci Quart., vol. 11 (1973), no. 1, 40-55.
Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,1).

Cf. A013982.

a:=proc(n,p,q) option remember:
if n<=p then 1
elif n<=q then a(n-1,p,q)+a(n-p,p,q)
else add(a(n-k,p,q),k=p..q) fi end:
seq(a(n,2,5),n=0..100); # Robert FERREOL, Oct 05 2017

CoefficientList[ Series[(1 + x)/(1 - x^2 - x^3 - x^4 - x^5), {x, 0, 40}], x]
LinearRecurrence[{0,1,1,1,1},{1,1,1,2,3},40] (* Harvey P. Dale, Sep 01 2014 *)

x='x+O('x^99); Vec((1+x)/(1-x^2-x^3-x^4-x^5)) \\ Altug Alkan, Oct 06 2017

a(n) = a(n-1) + a(n-2) - a(n-6);
G.f.: = (1 + x)/(1 - x^2 - x^3 - x^4 - x^5).
a(n) = A013982(n) + A013982(n-1). - R. J. Mathar, Nov 29 2011

cp's OEIS Frontend

A109544 Expansion of (1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Maxima

PARI

Formula