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A038508 Expansion of (1-2*x-x^2)/((1-2*x)*(1-2*x+2*x^2)). 2
1, 2, 5, 12, 30, 76, 196, 512, 1352, 3600, 9648, 25984, 70240, 190400, 517184, 1406976, 3831936, 10445056, 28488448, 77735936, 212186624, 579320832, 1581966336, 4320477184, 11800692736, 32233951232 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of (s(0), s(1), ..., s(n+1)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n+1, s(0) = 1, s(n+1) = 2. - Herbert Kociemba, Jun 17 2004

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (4,-2,-4).

FORMULA

a(n)=(3*2^(n+1) - Sqrt[3](1-Sqrt[3])^(n+1) + Sqrt[3](1+Sqrt[3])^(n+1))/12 - Herbert Kociemba, Jun 17 2004

2*a(n) = 2^n +  A002605(n+1). - R. J. Mathar, Sep 11 2019

PROG

(PARI) Vec((1-2*x-x^2)/(1-4*x+2*x^2+4*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

First differences are in A094297.

Sequence in context: A108360 A051163 A051450 * A105695 A244884 A002026

Adjacent sequences:  A038505 A038506 A038507 * A038509 A038510 A038511

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified January 21 16:22 EST 2020. Contains 331114 sequences. (Running on oeis4.)