

A094831


Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 9 and s(i)  s(i1) = 1 for i = 1,2,....,2n, s(0) = 3, s(2n) = 3.


3



1, 2, 6, 19, 62, 207, 703, 2417, 8382, 29242, 102431, 359790, 1266103, 4460939, 15730497, 55500634, 195890270, 691566411, 2441886670, 8623112591, 30453261927, 107553444913, 379864424726, 1341658806066, 4738726458775
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OFFSET

0,2


COMMENTS

In general a(n) = (2/m)*Sum(r,1,m1,Sin(r*j*Pi/m)Sin(r*k*Pi/m)(2Cos(r*Pi/m))^(2n)) counts (s(0), s(1), ..., s(2n)) such that 0 < s(i) < m and s(i)s(i1) = 1 for i = 1,2,....,2n, s(0) = j, s(2n) = k.
A comparison of their recurrence relations shows that this sequence is the even bisection of A188048.  John Blythe Dobson, Jun 20 2015


LINKS

Table of n, a(n) for n=0..24.
Index entries for linear recurrences with constant coefficients, signature (6,9,1)


FORMULA

a(n) = (2/9) * Sum_{r=1..8} (sin(r*Pi/3)^2*(2*cos(r*Pi/9))^(2*n)).
a(n) = 6*a(n1)  9*a(n2) + a(n3).
G.f.: (14*x+3*x^2)/(16*x+9*x^2x^3).


PROG

(PARI) Vec((14*x+3*x^2)/(16*x+9*x^2x^3) + O(x^30)) \\ Michel Marcus, Jun 21 2015


CROSSREFS

Sequence in context: A148466 A094817 A033565 * A033193 A071738 A026012
Adjacent sequences: A094828 A094829 A094830 * A094832 A094833 A094834


KEYWORD

nonn


AUTHOR

Herbert Kociemba, Jun 13 2004


STATUS

approved



