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A255630 Number of n-length ternary words avoiding runs of zeros of length 1 (mod 3). 4
1, 2, 5, 13, 32, 79, 197, 490, 1217, 3025, 7520, 18691, 46457, 115474, 287021, 713413, 1773248, 4407559, 10955357, 27230458, 67683593, 168233257, 418157888, 1039366555, 2583432881, 6421339426, 15960778517, 39671855677, 98607729632 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (2,0,3).

FORMULA

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

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

a(n) = A099525(n)+A099525(n-2). - R. J. Mathar, Aug 07 2015

MATHEMATICA

RecurrenceTable[{a[0] == 1, a[2] == 2,  a[3] == 5,  a[n] == 2* a[n - 1] +  3*a[n - 3]}, a[n], {n, 0, 29}]

CROSSREFS

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

Sequence in context: A098586 A199812 A255170 * A298535 A110320 A219230

Adjacent sequences:  A255627 A255628 A255629 * A255631 A255632 A255633

KEYWORD

nonn,easy

AUTHOR

Milan Janjic, Feb 28 2015

STATUS

approved

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Last modified February 21 07:18 EST 2018. Contains 299390 sequences. (Running on oeis4.)