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A255814 Numbers of words on {0,1,2,3,4,} having no isolated zeros. 1
1, 4, 17, 73, 313, 1341, 5745, 24613, 105449, 451773, 1935521, 8292309, 35526553, 152205613, 652091089, 2793739205, 11969154121, 51279178141, 219694231041, 941231059125, 4032495084025, 17276328107789, 74016584439345, 317107590101669 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4,4).

FORMULA

a(n+3) = 5*a(n+2) - 4*a(n+1)+ 4*a(n) with n>=0, a(0) = 1, a(1) = 4, a(2) = 17.

G.f.: (-1 + x - x^2)/(-1 + 5*x - 4*x^2 + 4*x^3). - R. J. Mathar, Nov 07 2015

MATHEMATICA

RecurrenceTable[{a[0] == 1, a[1] == 4,  a[2]== 17, a[n] == 5 a[n - 1] - 4 a[n - 2] + 4 a[n - 3]}, a[n], {n, 0, 23}]

LinearRecurrence[{5, -4, 4}, {1, 4, 17}, 100] (* G. C. Greubel, Jun 02 2016 *)

CoefficientList[Series[(-1 + x - x^2) / (-1 + 5 x -4 x^2 + 4 x^3), {x, 0, 33}], x] (* Vincenzo Librandi, Feb 26 2018 *)

PROG

(MAGMA)  I:=[1, 4, 17]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+4*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 26 2018

CROSSREFS

Cf. A255116, A255118, A254658, A254660, A255633, A255630.

Sequence in context: A289159 A083330 A255632 * A095940 A018902 A184700

Adjacent sequences:  A255811 A255812 A255813 * A255815 A255816 A255817

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Mar 07 2015

STATUS

approved

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Last modified June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)