A038508 Expansion of (1-2*x-x^2)/((1-2*x)*(1-2*x+2*x^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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

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

Crossrefs

First differences are in A094297.

Cf. A002605.

Programs

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

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

a(n) = 4*a(n-1)-2*a(n-2)-4*a(n-3). - Wesley Ivan Hurt, May 14 2021