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A093652 Let a(1) = 1, a(2) = 2, a(3) = 7, a(4) = 15 and for n >= 5 set a(n) = (n*b(n) - b(n-2)) / 2, where b(n) = 4*b(n-2) - b(n-4) for n >= 5 and b(1) = 1, b(2) = 2, b(3) = 5, b(4) = 8.

%I A093652 #47 Oct 24 2023 03:21:35
%S A093652 1,2,7,15,45,86,239,433,1157,2034,5307,9151,23497,39974,101467,170913,
%T A093652 430089,718946,1796975,2985775,7422437,12272502,30373191,50016721,
%U A093652 123327373,202395986,497484067,814061151,1995542913,3257222726,7965875891,12973832257,31663779857
%N A093652 Let a(1) = 1, a(2) = 2, a(3) = 7, a(4) = 15 and for n >= 5 set a(n) = (n*b(n) - b(n-2)) / 2, where b(n) = 4*b(n-2) - b(n-4) for n >= 5 and b(1) = 1, b(2) = 2, b(3) = 5, b(4) = 8.
%C A093652 a(n)/b(n) gives the ohm value of a ladder of unit resistors measured from opposite corners. The ladder is best described as a line of n squares, where every segment has a resistance of 1 ohm.
%C A093652 1/(n - 2*a(n)/b(n)) approaches 2 + sqrt(3) as n increases.
%H A093652 Harri Aaltonen, Apr 18 2008, <a href="/A093652/b093652.txt">Table of n, a(n) for n = 1..50</a> [a(49) corrected by _Georg Fischer_, Mar 13 2020]
%H A093652 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,8,0,-18,0,8,0,-1).
%H A093652 <a href="/index/Res#resistances">Index to sequences related to resistances</a>.
%F A093652 Conjecture: b(n) = A082630(n). If true, we can write a(n) = (n*A082630(n) - A082630(n-2)) / 2.
%F A093652 From _Colin Barker_, Dec 20 2019: (Start)
%F A093652 G.f.: x*(1 + 2*x - x^2 - x^3 + 7*x^4 + 2*x^5 - 3*x^6 - x^7) / (1 - 4*x^2 + x^4)^2.
%F A093652 a(n) = 8*a(n-2) - 18*a(n-4) + 8*a(n-6) - a(n-8) for n>8.
%F A093652 (End)
%p A093652 a_list := proc(last) local B, C, k;
%p A093652    B := [1,2,5, 8];
%p A093652    C := [1,2,7,15];
%p A093652    for k from 5 to last do
%p A093652       B := [op(B), 4*B[k-2]-B[k-4]];
%p A093652       C := [op(C), (k*B[k]-B[k-2])/2];
%p A093652    od;
%p A093652 C end:
%p A093652 a_list(50); # After _Harri Aaltonen_, _Peter Luschny_, Mar 14 2020
%t A093652 LinearRecurrence[{0, 8, 0, -18, 0, 8, 0, -1}, {1, 2, 7, 15, 45, 86, 239, 433}, 50] (* _Jean-François Alcover_, Oct 24 2023 *)
%Y A093652 Cf. A082630.
%K A093652 nonn,easy
%O A093652 1,2
%A A093652 _Harri Aaltonen_, May 15 2004, Apr 12 2008
%E A093652 Edited by _Peter Luschny_, Jun 14 2021