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

1,3

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).

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)

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 *)

Prog

(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
(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

Crossrefs

Cf. A065261.

Sequence in context: A010483 A003671 A318379 * A198738 A051356 A188933

Adjacent sequences: A065259 A065260 A065261 * A065263 A065264 A065265

Keyword

nonn,easy

Author

Antti Karttunen, Oct 28 2001

Status

approved