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First differences of A052980.
2

%I #34 Apr 18 2022 10:46:26

%S 0,1,3,6,13,29,64,141,311,686,1513,3337,7360,16233,35803,78966,174165,

%T 384133,847232,1868629,4121391,9090014,20048657,44218705,97527424,

%U 215103505,474425715,1046378854,2307861213

%N First differences of A052980.

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

%C Ternary words of length n-1 with subwords (0,1), (1,1) and (1,2) not allowed. - _Olivier Gérard_, Aug 28 2012

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1).

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

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

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

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

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

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

%t LinearRecurrence[{2,0,1},{0,1,3},30] (* _Harvey P. Dale_, Sep 04 2017 *)

%Y Cf. A008998, A052980, A064353, A078061.

%K nonn

%O 0,3

%A _Philippe Deléham_, Jul 22 2012