A107299 a(n) = 4*a(n-1)-2*a(n-2)-3*a(n-3)+2*a(n-4), n>5.

3, 3, 10, 29, 94, 292, 913, 2844, 8862, 27605, 85990, 267852, 834337, 2598884, 8095286, 25216069, 78545726, 244662676, 762101617, 2373876076, 7394404494, 23032886325, 71745311318, 223480011292, 696119572545, 2168348106292

Offset

0,1

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (4, -2, -3, 2).

Formula

G.f.: (2*x-1)*(x^4-2*x^2-3*x+3)/( (x-1) * (2*x^3-x^2-3*x+1)) . [Sep 28 2009]

Mathematica

b1 = x /. NSolve[x^3 - 3*x^2 - x + 2 == 0, x][[1]] b2 = x /. NSolve[x^3 - 3*x^2 - x + 2 == 0, x][[2]] b3 = x /. NSolve[x^3 - 3*x^2 - x + 2 == 0, x][[3]] digits = 25 a = Table[N[3*(b3^n + b1^n + b2^n)/(b3 + b2 + b1)], {n, 0, digits}] Floor[a]
LinearRecurrence[{4, -2, -3, 2}, {3, 3, 10, 29, 94, 292}, 30] (* Harvey P. Dale, Aug 21 2020 *)

Crossrefs

Sequence in context: A019153 A049975 A019168 * A298899 A205388 A121446

Adjacent sequences: A107296 A107297 A107298 * A107300 A107301 A107302

Keyword

nonn,easy

Author

Roger L. Bagula, May 20 2005

Extensions

Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009

Status

approved