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A214260 First differences of A052980. 2
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 (list; graph; refs; listen; history; text; internal format)
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)/(1-2x-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. A052980, A008998, A064353

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

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Last modified February 25 04:05 EST 2018. Contains 299630 sequences. (Running on oeis4.)