A287832 Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 1.

1, 11, 101, 929, 8545, 78599, 722973, 6650087, 61169169, 562649373, 5175390189, 47604538285, 437878494689, 4027716327495, 37047945974857, 340776308298291, 3134546038698889, 28832341420057365, 265207115001514409, 2439441626426418609, 22438596523731989473

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (11,-14,-28,39,9,-10).

Formula

For n>6, a(n) = 11*a(n-1) - 14*a(n-2) - 28*a(n-3) + 39*a(n-4) + 9*a(n-5) - 10*a(n-6), a(0)=1, a(1)=11, a(2)=101, a(3)=929, a(4)=8545, a(5)=78599, a(6)=722973.

G.f.: (1 - 6*x^2 + 9*x^4 - 2*x^6)/(1 - 11*x + 14*x^2 + 28*x^3 - 39*x^4 - 9*x^5 + 10*x^6).

Mathematica

LinearRecurrence[{11, -14, -28, 39, 9, -10}, {1, 11, 101, 929, 8545, 78599, 722973}, 20]

Prog

(Python)
def a(n):
.if n in [0, 1, 2, 3, 4, 5, 6]:
..return [1, 11, 101, 929, 8545, 78599, 722973][n]
.return 11*a(n-1) - 14*a(n-2) - 28*a(n-3) + 39*a(n-4) + 9*a(n-5) - 10*a(n-6)

Crossrefs

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

Sequence in context: A163146 A037550 A138894 * A122105 A332853 A289850

Adjacent sequences: A287829 A287830 A287831 * A287833 A287834 A287835

Keyword

nonn,easy

Author

David Nacin, Jun 07 2017

Status

approved