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

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,4).

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

a(n) = A135032(n-1)+A135032(n). - R. J. Mathar, Apr 07 2022

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 *)

Prog

(Magma) [n le 1 select 7^n else 6*Self(n)+4*Self(n-1): n in [0..25]]; // Bruno Berselli, Feb 03 2015
(PARI) Vec((1 + x)/(1 - 6*x - 4*x^2) + O(x^30)) \\ Colin Barker, Jan 22 2017

Crossrefs

Cf. A055099, A126473, A126501, A126528, A135032, A190976 (shifted bin. trans).

Sequence in context: A081894 A128597 A190972 * A258340 A244265 A240722

Adjacent sequences: A254598 A254599 A254600 * A254602 A254603 A254604

Keyword

nonn,easy

Author

Milan Janjic, Feb 02 2015

Status

approved