A082587 - OEIS

A082587

G.f.: (3+x+x^2+2*x^3)/(1-x^2-x^4).

3, 1, 4, 3, 7, 4, 11, 7, 18, 11, 29, 18, 47, 29, 76, 47, 123, 76, 199, 123, 322, 199, 521, 322, 843, 521, 1364, 843, 2207, 1364, 3571, 2207, 5778, 3571, 9349, 5778, 15127, 9349, 24476, 15127, 39603, 24476, 64079, 39603, 103682, 64079, 167761, 103682, 271443, 167761

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OFFSET

0,1

COMMENTS

a(2*n) = A000204(n+2), a(2*n+1) = A000204(n+1); a(2*n+1) = a(2*n-1) for n > 0. Reinhard Zumkeller, Aug 03 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,1,0,1).

FORMULA

a(n) = A000204(floor(n/2) + 2 - n mod 2). - Reinhard Zumkeller, Aug 03 2013

MATHEMATICA

CoefficientList[Series[(3+x+x^2+2x^3)/(1-x^2-x^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 1, 0, 1}, {3, 1, 4, 3}, 50] (* Harvey P. Dale, Apr 09 2023 *)

PROG

(Haskell)

import Data.List (transpose)

a082587 n = a082587_list !! n

a082587_list = concat $ transpose [tail a000204_list, a000204_list]

-- Reinhard Zumkeller, Aug 03 2013

CROSSREFS

Sequence in context: A262214 A340760 A035626 * A364670 A060043 A298254

Adjacent sequences: A082584 A082585 A082586 * A082588 A082589 A082590

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 13 2003

STATUS

approved