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A254659
Numbers of words on alphabet {0,1,...,8} with no subwords ii, where i is from {0,1,2,3}.
1
1, 9, 77, 661, 5673, 48689, 417877, 3586461, 30781073, 264180889, 2267352477, 19459724261, 167014556473, 1433415073089, 12302393367077, 105586222302061, 906201745251873, 7777545073525289, 66751369314461677, 572898679883319861, 4916946285638867273
OFFSET
0,2
COMMENTS
a(n) is the number of nonary sequences of length n such that no two consecutive terms have distance 7. - David Nacin, May 31 2017
FORMULA
G.f.: (1 + x)/(1 - 8*x - 5*x^2).
a(n) = 8*a(n-1) + 5*a(n-2) with n>1, a(0) = 1, a(1) = 9.
a(n) = ((4-r)^n*(-5+r) + (4+r)^n*(5+r)) / (2*r), where r=sqrt(21). - Colin Barker, Jan 22 2017
MATHEMATICA
RecurrenceTable[{a[0] == 1, a[1] == 9, a[n] == 8 a[n - 1] + 5 a[n - 2]}, a[n], {n, 0, 20}]
PROG
(Magma) [n le 1 select 9^n else 8*Self(n)+5*Self(n-1): n in [0..20]];
(PARI) Vec((1 + x)/(1 - 8*x -5*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017
KEYWORD
nonn,easy
AUTHOR
Milan Janjic, Feb 04 2015
STATUS
approved