The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A001614 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A001614

Connell sequence: 1 odd, 2 even, 3 odd, ...
(history; published version)

#104 by N. J. A. Sloane at Sat Oct 19 22:06:00 EDT 2024

STATUS

proposed

approved

#103 by Stefano Spezia at Sat Oct 19 12:36:40 EDT 2024

STATUS

editing

proposed

#102 by Stefano Spezia at Sat Oct 19 12:36:36 EDT 2024

FORMULA

G.f. : 2*x/(1-x)^2 - (x/(1-x))*Sum_{n>=0} x^(n*(n+1)/2) = 2*x/(1-x)^2 - (Theta2(0,x^(1/2)))*x^(7/8)/(2*(1-x)) where Theta2 is a Jacobi theta function.

STATUS

proposed

editing

#101 by Stefano Spezia at Sat Oct 19 12:36:10 EDT 2024

STATUS

editing

proposed

#100 by Stefano Spezia at Sat Oct 19 12:36:05 EDT 2024

FORMULA

G.f. 2*x/(1-x)^2 - (x/(1-x))*sum(Sum_{n>=0, } x^(n*(n+1)/2) = 2*x/(1-x)^2 - (Theta2(0,x^(1/2)))*x^(7/8)/(2*(1-x)) where Theta2 is a Jacobi theta function.

= 2*x/(1-x)^2 - (Theta2(0,x^(1/2)))*x^(7/8)/(2*(1-x)) where Theta2 is a Jacobi theta function.

a(n) = 2*n-1 - Sum(_{i=0..n-2, } A023531(i)). (End)

STATUS

proposed

editing

#99 by Chai Wah Wu at Sat Oct 19 11:10:03 EDT 2024

STATUS

editing

proposed

#98 by Chai Wah Wu at Sat Oct 19 11:09:25 EDT 2024

FORMULA

a(n) = 3*n-A014132(n). - Chai Wah Wu, Oct 19 2024

CROSSREFS

Cf. A014132, A057211, A023531.

STATUS

approved

editing

#97 by Joerg Arndt at Wed Jul 27 02:20:18 EDT 2022

STATUS

reviewed

approved

#96 by Michel Marcus at Wed Jul 27 00:56:05 EDT 2022

STATUS

proposed

reviewed

#95 by Jon E. Schoenfield at Tue Jul 26 18:32:47 EDT 2022

STATUS

editing

proposed