A065262 The nonpositive side (-1, -2, -3, ...) of the site swap sequence A065261. The bisection of odd terms of A065261.
1, 1, 5, 2, 9, 3, 13, 4, 17, 5, 21, 6, 25, 7, 29, 8, 33, 9, 37, 10, 41, 11, 45, 12, 49, 13, 53, 14, 57, 15, 61, 16, 65, 17, 69, 18, 73, 19, 77, 20, 81, 21, 85, 22, 89, 23, 93, 24, 97, 25, 101, 26, 105, 27, 109, 28, 113, 29, 117, 30, 121, 31, 125, 32, 129, 33, 133, 34, 137, 35
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
Crossrefs
Cf. A065261.
Programs
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Magma
I:=[1, 1, 5, 2]; [n le 4 select I[n] else 2*Self(n-2)-Self(n-4) : n in [1..100]]; // Wesley Ivan Hurt, Dec 06 2015
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Maple
a:=proc(n) option remember; if n=1 then 1 elif n=2 then 1 elif n=3 then 5 elif n=4 then 2 else 2*a(n-2)-a(n-4); fi; end: seq(a(n), n=1..100); # Wesley Ivan Hurt, Dec 06 2015
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Mathematica
CoefficientList[Series[(3*x^2 + x + 1)/(x^2 - 1)^2, {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 2, 0, -1}, {1, 1, 5, 2}, 100] (* Wesley Ivan Hurt, Dec 06 2015 *) -
PARI
Vec(x*(3*x^2+x+1) / ((x-1)^2*(x+1)^2) + O(x^100)) \\ Michel Marcus, Dec 06 2015
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PARI
vector(100, n, n - sum(i=1, n, ceil((-1)^i*(2*n-3+i)/2 ))) \\ Altug Alkan, Dec 06 2015
Formula
G.f.: x*(3*x^2+x+1) / ((x-1)^2*(x+1)^2). [Colin Barker, Feb 18 2013]
From Wesley Ivan Hurt, Dec 06 2015: (Start)
a(n) = 2*a(n-2)-a(n-4) for n>4.
a(n) = n - Sum_{i=1..n} ceiling( (-1)^i*(2*n-3+i)/2 ). (End)
Comments