The On-Line Encyclopedia of Integer Sequences (OEIS)

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A246416

A permutation of essentially the duplicate nonnegative numbers: a(4n) = n + 1/2 - (-1)^n/2, a(2n+1) = a(4n+2) = 2n+1.
(history; published version)

#60 by Charles R Greathouse IV at Thu Sep 08 08:46:09 EDT 2022

PROG

(MAGMAMagma) I:=[0, 1, 1, 3, 2, 5, 3, 7, 2, 9, 5, 11, 4, 13, 7, 15, 4, 17, 9, 19, 6, 21, 11, 23]; [n le 24 select I[n] else 3*Self(n-8)-3*Self(n-16)+Self(n-24): n in [1..80]]; // Vincenzo Librandi, Oct 15 2014

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#59 by Susanna Cuyler at Wed May 02 09:27:44 EDT 2018

STATUS

proposed

approved

#58 by Jon E. Schoenfield at Tue May 01 23:34:35 EDT 2018

STATUS

editing

proposed

#57 by Jon E. Schoenfield at Tue May 01 23:34:32 EDT 2018

NAME

A permutation of essentially the duplicate nonnegative numbers: a(4n) = n + 1/2 - (-1)^n/2, a(2n+1) = a(4n+2) = 2n+1.

COMMENTS

A permutation of A004526 (n > 0).

0 is at its own place. Distance between the two (2*k+1)'s: 2*k+1 terms. 0 is in position 0, the first 1 in position 1, the second 1 in position 2, the first 2 in position 4, the second 2 in position 8. Hence : , r(n) = 0, 1, 2, 4, 8, 3, 6, 12, 16, 5, 10, 20, 24, ... , , a permutation of A001477. See A225055. The recurrence r(n) = r(n-4) + r(n-8) - r(n-12) is the same as for a(n).

A061037(n+3) is divisible by a(n+5) (= 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 3, ...). Hence a link, via A212831 and A214282, between the Catalan numbers A000108 and the Balmer series.

STATUS

proposed

editing

#56 by G. C. Greubel at Tue May 01 23:10:17 EDT 2018

STATUS

editing

proposed

#55 by G. C. Greubel at Tue May 01 23:10:05 EDT 2018

LINKS

G. C. Greubel, <a href="/A246416/b246416.txt">Table of n, a(n) for n = 0..5000</a>

STATUS

approved

editing

#54 by Charles R Greathouse IV at Sat Jun 13 00:55:05 EDT 2015

LINKS

<a href="/index/Rec#order_12">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,0,0,1,0,0,0,-1).

Discussion

Sat Jun 13

00:55

OEIS Server: https://oeis.org/edit/global/2439

#53 by Harvey P. Dale at Mon Mar 23 11:58:40 EDT 2015

STATUS

editing

approved

#52 by Harvey P. Dale at Mon Mar 23 11:58:34 EDT 2015

MATHEMATICA

LinearRecurrence[{0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1}, {0, 1, 1, 3, 2, 5, 3, 7, 2, 9, 5, 11}, 70] (* Harvey P. Dale, Mar 23 2015 *)

STATUS

approved

editing

#51 by Bruno Berselli at Wed Oct 15 06:15:39 EDT 2014

STATUS

editing

approved