The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A114113 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A114113

a(n) = sum{k=1 to n} (A114112(k)). (For n>=2, a(n) = sum{k=1 to n} (A014681(k)) =sum{k=1 to n} (A103889(k)).).
(history; published version)

#41 by Charles R Greathouse IV at Thu Sep 08 08:45:23 EDT 2022

PROG

(MAGMAMagma) I:=[1, 3, 7, 10, 16]; [n le 5 select I[n] else 2*Self(n-1)-2*Self(n-3)+Self(n-4): n in [1..60]]; // Vincenzo Librandi, Mar 13 2018

Discussion

Thu Sep 08

08:45

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

#40 by Michael De Vlieger at Tue May 24 10:15:46 EDT 2022

STATUS

reviewed

approved

#39 by Joerg Arndt at Tue May 24 10:01:20 EDT 2022

STATUS

proposed

reviewed

#38 by Michel Marcus at Tue May 24 09:16:15 EDT 2022

STATUS

editing

proposed

#37 by Michel Marcus at Tue May 24 09:16:00 EDT 2022

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2, 0, -2, 1).

FORMULA

From R. J. Mathar, Nov 04 2008: (Start)

a(n) = A026035(n+1) - A026035(n), n>1.

a(n) = A026035(n+1)-A026035(n), n>1. G.f.: x(1+x+x^2-2x^3+x^4)/((1+x)(1-x)^3). a(n)=2*a(n-1)-2*a(n-3)+a(n-4), n>5. [_R. J. Mathar_, Nov 04 2008]

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4), n>5. (End)

STATUS

proposed

editing

#36 by Chai Wah Wu at Tue May 24 09:12:34 EDT 2022

STATUS

editing

proposed

#35 by Chai Wah Wu at Tue May 24 09:12:07 EDT 2022

PROG

(Python)

def A114113(n): return 1 if n == 1 else (m:=n//2)*(n+1) + (n+1-m)*(n-2*m) # Chai Wah Wu, May 24 2022

STATUS

approved

editing

#34 by Bruno Berselli at Tue Mar 13 04:04:10 EDT 2018

STATUS

proposed

approved

#33 by Vincenzo Librandi at Tue Mar 13 03:17:05 EDT 2018

STATUS

editing

proposed

#32 by Vincenzo Librandi at Tue Mar 13 03:16:53 EDT 2018

COMMENTS

Needs a b-file. - N. J. A. Sloane, Mar 12 2018