A019489 -id:A019489 - cp's OEIS frontend

A077852 Expansion of (1-x)^(-1)/(1-2*x-x^3).

1, 3, 7, 16, 36, 80, 177, 391, 863, 1904, 4200, 9264, 20433, 45067, 99399, 219232, 483532, 1066464, 2352161, 5187855, 11442175, 25236512, 55660880, 122763936, 270764385, 597189651, 1317143239, 2905050864, 6407291380, 14131726000, 31168502865, 68744297111

Offset: 0

N. J. A. Sloane, Nov 17 2002

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-1).

Cf. A019489. - R. J. Mathar, Sep 19 2008

a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-1|1|-2|3>>^n)[4,4]:
seq(a(n), n=0..30);  # Alois P. Heinz, Nov 12 2017

CoefficientList[Series[(1-x)^(-1)/(1-2x-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{3,-2,1,-1},{1,3,7,16},40] (* Harvey P. Dale, Oct 05 2012 *)

From R. J. Mathar, May 15 2008: (Start)
a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) - a(n-4).
a(n+1) - a(n) = A008998(n+1). (End)
a(n) = 2*a(n-1) + a(n-3) + 1. - Greg Dresden, Apr 04 2021

A022040 Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(16,36).

Original entry on oeis.org

16, 36, 80, 177, 391, 863, 1904, 4200, 9264, 20433, 45067, 99399, 219232, 483532, 1066464, 2352161, 5187855, 11442175, 25236512, 55660880, 122763936, 270764385, 597189651, 1317143239, 2905050864, 6407291380, 14131726000, 31168502865, 68744297111

Offset: 0

R. K. Guy

nonn

Not to be confused with the Pisot T(16,32) sequence, which is essentially A000079. - R. J. Mathar, Feb 13 2016

Apparently a(n) = A019489(n+2) = A077852(n+3) (Barker's recurrence) for n >= 0. - Georg Fischer, Mar 23 2019

Colin Barker, Table of n, a(n) for n = 0..1000
D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
Index entries for Pisot sequences

Cf. A019489, A077852.

T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=ceil(a[n-1]^2/a[n-2])-1); a
T(16, 36, 30) \\ Colin Barker, Feb 16 2016

Empirical G.f.: (16-12*x+4*x^2-7*x^3)/(1-3*x+2*x^2-x^3+x^4). - Colin Barker, Feb 16 2012

a(n+1) = ceiling(a(n)^2/a(n-1))-1 for n>0. - Bruno Berselli, Feb 15 2016

cp's OEIS Frontend

A077852 Expansion of (1-x)^(-1)/(1-2*x-x^3).

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