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A014010 Linear recursion relative of Shallit sequence S(2,6). 2
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 (list; graph; refs; listen; history; text; internal format)
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).

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

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Last modified July 21 00:49 EDT 2019. Contains 325189 sequences. (Running on oeis4.)