

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(n1) + a(n2)  10*a(n3), 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) = 498 = 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(n1)+a(n2)10*a(n3)


CROSSREFS

Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473.
Cf. A287804A287819.
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



