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A287810 Number of septenary sequences of length n such that no two consecutive terms have distance 3. 0
1, 7, 41, 241, 1417, 8333, 49005, 288193, 1694833, 9967141, 58615749, 344713305, 2027224169, 11921900829, 70111496093, 412318635697, 2424804301985, 14260029486677, 83861794865077, 493182755657289, 2900358033942041, 17056713010658765, 100308808541321741 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (6, 1, -10).

FORMULA

For n>3, a(n) = 6*a(n-1) + a(n-2) - 10*a(n-3), a(0)=1, a(1)=7, a(2)=41, a(3)=241.

G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 6*x - x^2 + 10*x^3).

EXAMPLE

For n=2 the a(2) = 49-8 = 41 sequences contain every combination except these eight: 03, 30, 14, 41, 25, 52, 36, 63.

MATHEMATICA

LinearRecurrence[{6, 1, -10}, {1, 7, 41, 241}, 40]

PROG

(Python)

def a(n):

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

..return [1, 7, 41, 241][n]

.return 6*a(n-1)+a(n-2)-10*a(n-3)

CROSSREFS

Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473.

Cf. A287804-A287819.

Sequence in context: A002315 A141813 A088165 * A292035 A108983 A115137

Adjacent sequences:  A287807 A287808 A287809 * A287811 A287812 A287813

KEYWORD

nonn,easy

AUTHOR

David Nacin, Jun 01 2017

STATUS

approved

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Last modified December 14 07:15 EST 2018. Contains 318090 sequences. (Running on oeis4.)