A255815 Numbers of words on {0,1,2,3,4,5} having no isolated zeros.

1, 5, 26, 136, 711, 3716, 19421, 101501, 530481, 2772486, 14490016, 75730071, 395792776, 2068556381, 10811024761, 56502330541, 295301641346, 1543353319176, 8066123361031, 42156481777036, 220325040452941, 1151498450637621

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 (6,-5,5).

Formula

a(n+3) = 6*a(n+2) - 5*a(n+1)+ 5*a(n) with n>=0, a(0) = 1, a(1) = 5, a(2) = 26.

G.f.: (-1 + x - x^2)/(-1 + 6*x - 5*x^2 + 5*x^3). - R. J. Mathar, Nov 07 2015

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 5,  a[2]== 26, a[n] == 6 a[n - 1] - 5 a[n - 2] + 5 a[n - 3]}, a[n], {n, 0, 21}]
LinearRecurrence[{6, -5, 5}, {1, 5, 26}, 100] (* G. C. Greubel, Jun 02 2016 *)

Crossrefs

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

Sequence in context: A255118 A052918 A255633 * A018903 A355361 A083331

Adjacent sequences: A255812 A255813 A255814 * A255816 A255817 A255818

Keyword

nonn,easy

Author

Milan Janjic, Mar 07 2015

Status

approved