A255814 Numbers of words on {0,1,2,3,4,} having no isolated zeros.

1, 4, 17, 73, 313, 1341, 5745, 24613, 105449, 451773, 1935521, 8292309, 35526553, 152205613, 652091089, 2793739205, 11969154121, 51279178141, 219694231041, 941231059125, 4032495084025, 17276328107789, 74016584439345, 317107590101669

Offset

0,2

Links

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

D. Birmajer, J. B. Gil, and M. D. Weiner, On the Enumeration of Restricted Words over a Finite Alphabet, J. Int. Seq. 19 (2016) # 16.1.3, example 11.

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 A344506

Adjacent sequences: A255811 A255812 A255813 * A255815 A255816 A255817

Keyword

nonn,easy

Author

Milan Janjic, Mar 07 2015

Status

approved