The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A164900 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A164900

a(2n) = 4*n*(n+1) + 3; a(2n+1) = 2*n*(n+2) + 3.
(history; published version)

#46 by N. J. A. Sloane at Sat Oct 19 22:07:40 EDT 2024

STATUS

proposed

approved

#45 by Stefano Spezia at Sat Oct 19 09:02:27 EDT 2024

STATUS

editing

proposed

#44 by Stefano Spezia at Sat Oct 19 08:28:30 EDT 2024

LINKS

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).

#43 by Stefano Spezia at Sat Oct 19 06:32:17 EDT 2024

FORMULA

E.g.f.: ((6 + 3*x + 2*x^2)*cosh(x) + (3 + 6*x + x^2)*sinh(x))/2. - Stefano Spezia, Oct 19 2024

STATUS

approved

editing

#42 by Michel Marcus at Tue Aug 09 12:04:58 EDT 2022

STATUS

reviewed

approved

#41 by Vaclav Kotesovec at Tue Aug 09 03:57:27 EDT 2022

STATUS

proposed

reviewed

#40 by Amiram Eldar at Tue Aug 09 02:28:47 EDT 2022

STATUS

editing

proposed

#39 by Amiram Eldar at Tue Aug 09 02:10:44 EDT 2022

LINKS

Kival Ngaokrajang, <a href="/A164900/a164900.pdf">Illustration of initial terms</a>.

CROSSREFS

Cf. A026741, A058331, A059100, A164845, A164897.

#38 by Amiram Eldar at Tue Aug 09 02:09:42 EDT 2022

FORMULA

From Amiram Eldar, Aug 09 2022: (Start)

a(n) = numerator(((n+1)^2 + 2)/2).

Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(2))*Pi/sqrt(2) + tanh(Pi/sqrt(2))*Pi/(2*sqrt(2)) - 1)/2. (End)

MATHEMATICA

LinearRecurrence[{0, 3, 0, -3, 0, 1}, {3, 3, 11, 9, 27, 19}, 50] (* Amiram Eldar, Aug 09 2022 *)

PROG

(MAGMAMagma) [((-1)^n+3)*(n^2+2*n+3)/4: n in [0..50]]; // Vincenzo Librandi, Aug 07 2011

STATUS

approved

editing

#37 by Bruno Berselli at Tue Jul 07 11:47:38 EDT 2015

STATUS

proposed

approved