A255632 - OEIS

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A255632

Number of n-length words on {0,1,2,3,4} avoiding runs of zeros of length 1 (mod 3).

1, 4, 17, 73, 312, 1333, 5697, 24348, 104057, 444713, 1900592, 8122653, 34714177, 148359668, 634051937, 2709778633, 11580912872, 49493911173, 211524537857, 904002715788, 3863480419017, 16511544365353, 70566191040352

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (4,0,5).

FORMULA

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

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

MATHEMATICA

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

CROSSREFS

Cf. A254598, A254602, A255115, A255117, A254601, A254663.

Sequence in context: A085732 A289159 A083330 * A255814 A095940 A018902

Adjacent sequences: A255629 A255630 A255631 * A255633 A255634 A255635

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Feb 28 2015

STATUS

approved