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

Author

Philippe Deléham, Jul 22 2012

Keywords

• nonn

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

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

Crossrefs

Cf. A008998, A052980, A064353, A078061.

Programs

Mathematica

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

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)).