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

Author

Milan Janjic, Feb 28 2015

Keywords

• nonn
• easy

Links

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

Crossrefs

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

Programs

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}]

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