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A065262 The nonpositive side (-1, -2, -3, ...) of the site swap sequence A065261. The bisection of odd terms of A065261. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 15 22:28 EST 2019. Contains 320138 sequences. (Running on oeis4.)