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Revision History for A014736

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A014736

Squares of odd triangular numbers.
(history; published version)

#30 by Joerg Arndt at Sun Mar 06 06:40:17 EST 2022

STATUS

reviewed

approved

#29 by Michel Marcus at Sun Mar 06 03:07:45 EST 2022

STATUS

proposed

reviewed

#28 by Amiram Eldar at Sun Mar 06 02:13:56 EST 2022

STATUS

editing

proposed

#27 by Amiram Eldar at Sun Mar 06 02:00:40 EST 2022

CROSSREFS

Cf. A000217, A006752, A014493, A014738.

#26 by Amiram Eldar at Sun Mar 06 02:00:08 EST 2022

PROG

(MAGMAMagma) [((2*n-1)*(2*n-1-(-1)^n))^2/4: n in [1..30]]; // Vincenzo Librandi, Mar 23 2012

#25 by Amiram Eldar at Sun Mar 06 01:59:43 EST 2022

FORMULA

From Amiram Eldar, Mar 06 2022: (Start)

Sum_{n>=0} 1/a(n) = (3*Pi-8)*Pi/4.

Sum_{n>=0} (-1)^n/a(n) = 4*(G - log(2)), where G is Catalan's constant (A006752). (End)

CROSSREFS

Cf. A000217, A006752, A014493.

STATUS

approved

editing

#24 by Susanna Cuyler at Wed Jul 24 07:51:05 EDT 2019

STATUS

proposed

approved

#23 by Alonso del Arte at Wed Jul 24 03:10:00 EDT 2019

STATUS

editing

proposed

#22 by Alonso del Arte at Wed Jul 24 03:09:45 EDT 2019

FORMULA

G.f.: x*(1 + 8*x + 212*x^2 + 184*x^3 + 726*x^4 + 184*x^5 + 212*x^6 + 8*x^7 + x^8)/((1 - x)^5*(1 + x)^4).

E.g.f.: (1 + x + 5*x^2 + 20*x^3 + 4*x^4)*cosh(x) - x*(1 - 17*x - 12*x^2 - 4*x^3)* sinh(x) - 1. (End)

#21 by Alonso del Arte at Wed Jul 24 03:08:34 EDT 2019

PROG

(Scala) ((1 to 78).scanLeft(0)(_ + _)).filter(_ % 2 == 1).map(n => n * n) // Alonso del Arte, Jul 24 2019

STATUS

proposed

editing