The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A303539 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A303539

Number of ordered pairs (k, m) with 0 <= k <= m such that n - binomial(2*k,k) - binomial(2*m,m) can be written as the sum of two squares.
(history; published version)

#29 by Michel Marcus at Thu Mar 02 13:01:36 EST 2023

STATUS

reviewed

approved

#28 by Wesley Ivan Hurt at Thu Mar 02 12:58:17 EST 2023

STATUS

proposed

reviewed

#27 by Sidney Cadot at Thu Mar 02 12:07:10 EST 2023

STATUS

editing

proposed

#26 by Sidney Cadot at Thu Mar 02 12:06:23 EST 2023

MATHEMATICA

c[n_]:=c[n]=Binomial[2n, n]；;

STATUS

approved

editing

Discussion

Thu Mar 02

12:07

Sidney Cadot: Replaced stray 'fullwidth semicolon' unicode character, '\uff1b', by a regular semicolon.

#25 by Alois P. Heinz at Sat Jul 20 21:04:55 EDT 2019

STATUS

proposed

approved

#24 by Jon E. Schoenfield at Sat Jul 20 19:49:49 EDT 2019

STATUS

editing

proposed

#23 by Jon E. Schoenfield at Sat Jul 20 19:49:28 EDT 2019

NAME

Number of ordered pairs (k, m) with 0 <= k <= m such that n - binombinomial(2*k,k) - binombinomial(2*m,m) can be written as the sum of two squares.

EXAMPLE

a(2) = 1 with 2 - binombinomial(2*0,0) - binombinomial(2*0,0) = 0^2 + 0^2.

a(3) = 2 with 3 - binombinomial(2*0,0) - binombinomial(2*0,0) = 0^2 + 1^2 and 3 - binombinomial(2*0,0) - binombinomial(2*1,1) = 0^2 + 0^2.

a(5) = 2 with 5 - binombinomial(2*0,0) - binombinomial(2*1,1) = 1^2 + 1^2 and 5 - binombinomial(2*1,1) - binombinomial(2*1,1) = 0^2 + 1^2.

STATUS

approved

editing

#22 by Alois P. Heinz at Wed Jun 27 15:50:09 EDT 2018

STATUS

proposed

approved

#21 by Zhi-Wei Sun at Wed Jun 27 12:37:45 EDT 2018

STATUS

editing

proposed

#20 by Zhi-Wei Sun at Wed Jun 27 12:37:13 EDT 2018

COMMENTS

a(n) > 0 for all n = 2..4*10^910.

STATUS

approved

editing