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

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,2).

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

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 7, a[n] == 6 a[n - 1] + 2 a[n - 2]}, a[n], {n, 0, 20}]

Prog

(PARI) Vec((1 + x) / (1 - 6*x -2*x^2) + O(x^30)) \\ Colin Barker, Jan 21 2017

Crossrefs

Cf. A135030, A126473, A126501, A126528, A254598, A254602.

Sequence in context: A027279 A099464 A355347 * A093738 A091127 A166775

Adjacent sequences: A254657 A254658 A254659 * A254661 A254662 A254663

Keyword

nonn,easy

Author

Milan Janjic, Feb 04 2015

Status

approved