A254660 Numbers of words on alphabet {0,1,...,6} with no subwords ii, where i is from {0,1,...,4}.
1, 7, 44, 278, 1756, 11092, 70064, 442568, 2795536, 17658352, 111541184, 704563808, 4450465216, 28111918912, 177572443904, 1121658501248, 7085095895296, 44753892374272, 282693546036224, 1785669060965888, 11279401457867776, 71247746869138432
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,2).
Programs
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Mathematica
RecurrenceTable[{a[0] == 1, a[1] == 7, a[n] == 6 a[n - 1] + 2 a[n - 2]}, a[n], {n, 0, 20}] LinearRecurrence[{6,2},{1,7},30] (* Harvey P. Dale, Sep 11 2024 *) -
PARI
Vec((1 + x) / (1 - 6*x -2*x^2) + O(x^30)) \\ Colin Barker, Jan 21 2017
Formula
G.f.: (1 + x)/(1 - 6*x -2*x^2).
a(n) = 6*a(n-1) + 2*a(n-2) with n>1, a(0) = 1, a(1) = 7.
a(n) = ((3-sqrt(11))^n*(-4+sqrt(11)) + (3+sqrt(11))^n*(4+sqrt(11))) / (2*sqrt(11)). - Colin Barker, Jan 21 2017