A014010 Linear recursion relative of Shallit sequence S(2,6).

2, 6, 19, 61, 196, 630, 2026, 6516, 20957, 67403, 216786, 697242, 2242518, 7212542, 23197479, 74609345, 239963764, 771788146, 2482278710, 7983677420, 25677658553, 82586271223, 265619709074, 854304581182, 2747673807690, 8837259590742, 28423008894139

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.

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.

Jeffrey Shallit, Problem B-686, Fib. Quart., 29 (1991), 85.

Index entries for linear recurrences with constant coefficients, signature (3,1,-1,1,-3).

Index entries for Pisot sequences

Formula

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

G.f.: ( 2-x^2-2*x^4 ) / ( (x-1)*(3*x^4+2*x^3+3*x^2+2*x-1) ).

Mathematica

LinearRecurrence[{3, 1, -1, 1, -3}, {2, 6, 19, 61, 196}, 30] (* Harvey P. Dale, Apr 21 2016 *)

Prog

(PARI) a2n=concat([ 2, 6, 19, 61, 196 ], vector(25)); a(n)=a2n[ n+1 ]; for(n=5, 29, a2n[ n+1 ]=3*a(n-1) + a(n-2) - a(n-3) + a(n-4) - 3*a(n-5))
(PARI) Vec((2-x^2-2*x^4)/((x-1)*(3*x^4+2*x^3+3*x^2+2*x-1)) + O(x^40)) \\ Colin Barker, Aug 09 2016

Crossrefs

There has been some confusion between A018906 and A014010. I think the descriptions are correct now, thanks to Michael Somos.

Different from A022041.

Sequence in context: A187276 A022041 A018906 * A022015 A138747 A052975

Adjacent sequences: A014007 A014008 A014009 * A014011 A014012 A014013

Keyword

nonn,easy

Author

R. K. Guy

Status

approved