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

Author

Antti Karttunen, Oct 28 2001

Keywords

• nonn
• easy

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

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

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

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

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)