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A287828 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 4. 0
1, 10, 88, 776, 6844, 60364, 532412, 4695892, 41417932, 365307620, 3222026092, 28418383780, 250651147340, 2210751960772, 19498910274028, 171981076403492, 1516879160180620, 13378927697789188, 118002614210453804, 1040787219651555556, 9179779989094951372 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9, 0, -14).

FORMULA

For n>3, a(n) = 9*a(n-1) - 14*a(n-3), a(0)=1, a(1)=10, a(2)=88, a(3)=776.

G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 9*x + 14*x^3).

MATHEMATICA

LinearRecurrence[{9, 0, -14}, {1, 10, 88, 776}, 30]

PROG

(Python)

def a(n):

.if n in [0, 1, 2, 3]:

..return [1, 10, 88, 776][n]

.return 9*a(n-1)-14*a(n-3)

CROSSREFS

Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287831.

Sequence in context: A125398 A273585 A165148 * A264320 A298134 A163030

Adjacent sequences:  A287825 A287826 A287827 * A287829 A287830 A287831

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 02 2017

STATUS

approved

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Last modified March 2 06:48 EST 2021. Contains 341744 sequences. (Running on oeis4.)