A214260 First differences of A052980.

0, 1, 3, 6, 13, 29, 64, 141, 311, 686, 1513, 3337, 7360, 16233, 35803, 78966, 174165, 384133, 847232, 1868629, 4121391, 9090014, 20048657, 44218705, 97527424, 215103505, 474425715, 1046378854, 2307861213

Offset

0,3

Comments

1 -> 123, 2 -> 12, 3 -> 2, starting with 1 gives the sequence: 1, 123, 123122, 1231221231212, ... the n-th term has a(n) digits.

Ternary words of length n-1 with subwords (0,1), (1,1) and (1,2) not allowed. - Olivier Gérard, Aug 28 2012

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (2,0,1).

Formula

Recurrence: a(0) = 0, a(1) = 1, a(2) = 3, a(n+1) = 2*a(n) + a(n-2).

G.f.: x*(1+x)/(1-2*x-x^3).

a(n) = A052980(n) + A052980(n-2) = A052980(n+1) - A052980(n).

a(n+1) = A078061(n)*(-1)^n.

a(0) = 0, a(n) = A008998(n-1) + A008998(n-2) for n>0.

a(n+1) = Sum_{k=0..n} C(n-k, floor(k/2))*2^(n-k-floor(k/2)).

Mathematica

LinearRecurrence[{2, 0, 1}, {0, 1, 3}, 30] (* Harvey P. Dale, Sep 04 2017 *)

Crossrefs

Cf. A008998, A052980, A064353, A078061.

Sequence in context: A106496 A052933 A071014 * A078061 A018909 A093128

Adjacent sequences: A214257 A214258 A214259 * A214261 A214262 A214263

Keyword

nonn

Author

Philippe Deléham, Jul 22 2012

Status

approved