A094825 Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,...,2n, s(0) = 1, s(2n) = 7.

1, 7, 35, 153, 624, 2444, 9333, 35055, 130207, 479941, 1759616, 6427032, 23412105, 85121783, 309062619, 1121050449, 4063463728, 14721293860, 53313308477, 193023319071, 698715633111, 2528895064637, 9152032060800, 33118656195888

Offset: 3

Author

Herbert Kociemba, Jun 15 2004

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 3..1792
• László Németh and László Szalay, Sequences Involving Square Zig-Zag Shapes, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
• Index entries for linear recurrences with constant coefficients, signature (8,-21,20,-5).

Crossrefs

Cf. A094865 (partial sums).

Programs

Mathematica

LinearRecurrence[{8,-21,20,-5},{1,7,35,153},30] (* Harvey P. Dale, Jan 16 2015 *)

Formula

a(n) = (1/5)*Sum_{r=1..9} sin(r*Pi/10)*sin(7*r*Pi/10)*(2*cos(r*Pi/10))^(2n).

a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4).

G.f.: x^3*(1-x)/( (1-3*x+x^2)*(1-5*x+5*x^2) ).

a(n) = -A001906(n)/2 + A020876(n)/10. - R. J. Mathar, Jun 24 2011