A122583 a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 6*a(n - 4) + 3*a(n - 5).
1, 1, 1, 1, 1, -3, -7, -3, 5, 25, 45, -3, -107, -191, -175, 253, 1045, 1189, -171, -3547, -7527, -4603, 11497, 33945, 40869, -10487, -141071, -248407, -120131, 421141, 1227961, 1332777, -726439, -5051271, -8369959, -3306635, 16738977, 43110597, 41391949, -33360335, -183387403, -283721435
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,-6,3).
Programs
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Magma
[n le 5 select 1 else Self(n-1) -2*Self(n-2) +Self(n-3) -6*Self(n-4) +3*Self(n-5): n in [1..50]]; // G. C. Greubel, Nov 28 2021
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Maple
A122583:= proc(n) option remember; if n <= 5 then 1; else A122583(n-1) -2*A122583(n-2)+A122583(n-3)+3*(-2*A122583(n-4)+A122583(n-5)); fi; end: seq(A122583(n), n=1..50) ; # R. J. Mathar, Sep 18 2007
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Mathematica
a[n_]:= a[n]= If[n<6, 1, a[n-1] -2*a[n-2] +a[n-3] -6*a[n-4] +3*a[n-5]]; Table[a[n], {n, 50}] LinearRecurrence[{1,-2,1,-6,3},{1,1,1,1,1},50] (* Harvey P. Dale, Jun 09 2025 *) -
Sage
@CachedFunction # a=A122583 def a(n): return 1 if (n<6) else a(n-1) -2*a(n-2) +a(n-3) -6*a(n-4) +3*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 +7*x^4)/(1 -x +2*x^2 -x^3 +6*x^4 -3*x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
Extensions
Edited by N. J. A. Sloane, Oct 01 2006
More terms from R. J. Mathar, Sep 18 2007
Comments