A255630 Number of n-length ternary words avoiding runs of zeros of length 1 (mod 3).

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

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