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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.
3
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
3,2
LINKS
László Németh and László Szalay, Sequences Involving Square Zig-Zag Shapes, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
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
MATHEMATICA
LinearRecurrence[{8, -21, 20, -5}, {1, 7, 35, 153}, 30] (* Harvey P. Dale, Jan 16 2015 *)
CROSSREFS
Cf. A094865 (partial sums).
Sequence in context: A223621 A215510 A240423 * A022635 A336602 A370391
KEYWORD
nonn
AUTHOR
Herbert Kociemba, Jun 15 2004
STATUS
approved