A287832 - OEIS

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

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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