A287833 Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 2.

1, 11, 103, 967, 9079, 85243, 800351, 7514541, 70554457, 662439857, 6219685951, 58396989455, 548292695881, 5147951686649, 48334414751849, 453814602701801, 4260891430727991, 40005754941255473, 375616336261903907, 3526683405274793053, 33112233522155404139

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10,-2,-37,16,19,1).

Formula

a(n) = 10*a(n-1) - 2*a(n-2) - 37*a(n-3) + 16*a(n-4) + 19*a(n-5) + a(n-6), a(0)=1, a(1)=11, a(2)=103, a(3)=967, a(4)=9079, a(5)=85243.

G.f.: (-1 - x + 5*x^2 + 4*x^3 - 6*x^4 - 3*x^5)/(-1 + 10*x - 2*x^2 - 37*x^3 + 16*x^4 + 19*x^5 + x^6).

Mathematica

LinearRecurrence[{10, -2, -37, 16, 19, 1}, {1, 11, 103, 967, 9079, 85243}, 20]

Prog

(Python)
def a(n):
.if n in [0, 1, 2, 3, 4, 5]:
..return [1, 11, 103, 967, 9079, 85243][n]
.return 10*a(n-1) - 2*a(n-2) - 37*a(n-3) + 16*a(n-4) + 19*a(n-5) + a(n-6)

Crossrefs

Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287839.

Sequence in context: A287302 A141915 A016133 * A155594 A077250 A356128

Adjacent sequences: A287830 A287831 A287832 * A287834 A287835 A287836

Keyword

nonn,easy

Author

David Nacin, Jun 07 2017

Status

approved