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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.

%I A094825 #19 Feb 12 2022 17:48:02
%S A094825 1,7,35,153,624,2444,9333,35055,130207,479941,1759616,6427032,
%T A094825 23412105,85121783,309062619,1121050449,4063463728,14721293860,
%U A094825 53313308477,193023319071,698715633111,2528895064637,9152032060800,33118656195888
%N 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.
%H A094825 Michael De Vlieger, <a href="/A094825/b094825.txt">Table of n, a(n) for n = 3..1792</a>
%H A094825 László Németh and László Szalay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Nemeth/nemeth8.html">Sequences Involving Square Zig-Zag Shapes</a>, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
%H A094825 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-21,20,-5).
%F A094825 a(n) = (1/5)*Sum_{r=1..9} sin(r*Pi/10)*sin(7*r*Pi/10)*(2*cos(r*Pi/10))^(2n).
%F A094825 a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4).
%F A094825 G.f.: x^3*(1-x)/( (1-3*x+x^2)*(1-5*x+5*x^2) ).
%F A094825 a(n) = -A001906(n)/2 + A020876(n)/10. - _R. J. Mathar_, Jun 24 2011
%t A094825 LinearRecurrence[{8,-21,20,-5},{1,7,35,153},30] (* _Harvey P. Dale_, Jan 16 2015 *)
%Y A094825 Cf. A094865 (partial sums).
%K A094825 nonn
%O A094825 3,2
%A A094825 _Herbert Kociemba_, Jun 15 2004