A254601 Numbers of n-length words on alphabet {0,1,...,6} with no subwords ii, where i is from {0,1,2}.
1, 7, 46, 304, 2008, 13264, 87616, 578752, 3822976, 25252864, 166809088, 1101865984, 7278432256, 48078057472, 317582073856, 2097804673024, 13857156333568, 91534156693504, 604633565495296, 3993938019745792, 26382162380455936, 174268726361718784
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (6,4).
Programs
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Magma
[n le 1 select 7^n else 6*Self(n)+4*Self(n-1): n in [0..25]]; // Bruno Berselli, Feb 03 2015
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Mathematica
RecurrenceTable[{a[0] == 1, a[1] == 7, a[n] == 6 a[n - 1] + 4 a[n - 2]}, a[n], {n, 0, 25}] LinearRecurrence[{6,4},{1,7},30] (* Harvey P. Dale, Oct 10 2017 *) -
PARI
Vec((1 + x)/(1 - 6*x - 4*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017
Formula
G.f.: (1 + x)/(1 - 6*x - 4*x^2).
a(n) = 6*a(n-1) + 4*a(n-2) with n>1, a(0) = 1, a(1) = 7.
a(n) = ((3-r)^n*(-4+r) + (3+r)^n*(4+r)) / (2*r), where r=sqrt(13). - Colin Barker, Jan 22 2017