Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Feb 12 2022 17:58:36
%S 1,6,27,110,428,1624,6069,22458,82555,302082,1101816,4009616,14567657,
%T 52865230,191684283,694609494,2515972324,9110338728,32981059485,
%U 119377761602,432046756571,1563510554986,5657752486512,20472344560800
%N Number of (s(0), s(1), ..., s(2n+1)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,...,2n+1, s(0) = 1, s(2n+1) = 6.
%C Diagonal of the square array A217593. - _Philippe Deléham_, Mar 28 2013
%H Michael De Vlieger, <a href="/A094788/b094788.txt">Table of n, a(n) for n = 2..1791</a>
%H 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 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-21,20,-5).
%F a(n) = (1/5)*Sum_{r=1..9} sin(r*Pi/10)*sin(3*r*Pi/5)*(2*cos(r*Pi/10))^(2*n+1).
%F a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4).
%F G.f.: -x^2*(-1+2*x) / ( (x^2-3*x+1)*(5*x^2-5*x+1) ).
%F a(n+2) = A217593(n,n+5). - _Philippe Deléham_, Mar 28 2013
%F 2*a(n) = A030191(n-1) - A001906(n). - _R. J. Mathar_, Nov 15 2019
%t Drop[CoefficientList[Series[-x^2*(-1 + 2 x)/((x^2 - 3 x + 1) (5 x^2 - 5 x + 1)), {x, 0, 25}], x], 2] (* _Michael De Vlieger_, Aug 04 2021 *)
%t LinearRecurrence[{8,-21,20,-5},{1,6,27,110},30] (* _Harvey P. Dale_, Aug 31 2021 *)
%o (PARI) Vec(x^2*(1-2*x)/(1-8*x+21*x^2-20*x^3+5*x^4)+O(x^66)) /* _Joerg Arndt_, Mar 29 2013 */
%K nonn,easy
%O 2,2
%A _Herbert Kociemba_, Jun 15 2004