A122582 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 2*a(n - 4) + a(n - 5).
1, 1, 1, 1, 1, -1, -3, -1, 3, 5, 3, -5, -13, -7, 13, 27, 15, -25, -61, -37, 57, 135, 81, -119, -297, -191, 257, 661, 431, -549, -1455, -991, 1169, 3225, 2257, -2497, -7115, -5145, 5299, 15725, 11715, -11261, -34709, -26623, 23829, 76603, 60479, -50361, -168997, -137173, 106105, 372655, 310905, -222951
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,-2,1,-2,1).
Programs
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Magma
[n le 5 select 1 else Self(n-1) -2*Self(n-2) +Self(n-3) -2*Self(n-4) +Self(n-5): n in [1..50]]; // G. C. Greubel, Nov 28 2021
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Mathematica
a[n_]:= a[n]= If[n<6, 1, a[n-1] -2*a[n-2] +a[n-3] -2*a[n-4] +a[n-5]]; Table[a[n], {n, 60}] Transpose[NestList[Flatten[{Rest[#],ListCorrelate[{1,-2,1,-2,1},#]}]&, {1,1,1,1,1},60]][[1]] (* Harvey P. Dale, Mar 21 2011 *) -
Sage
@CachedFunction # a=A122582 def a(n): return 1 if (n<6) else a(n-1) -2*a(n-2) +a(n-3) -2*a(n-4) +a(n-5) [a(n) for n in (1..50)] # G. C. Greubel, Nov 28 2021
Formula
G.f.: x*(1+2*x^2+x^3+3*x^4)/(1-x+2*x^2-x^3+2*x^4-x^5). - R. J. Mathar, May 12 2013
Extensions
Edited by N. J. A. Sloane, Oct 01 2006, Jan 01 2007
Comments