The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A175365 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A175365

Number of integer triples (x,y,z) satisfying |x|^3 + |y|^3 + |z|^3 = n, -n <= x,y,z <= n.
(history; published version)

#17 by Sean A. Irvine at Thu Aug 26 18:20:50 EDT 2021

STATUS

proposed

approved

#16 by Jon E. Schoenfield at Sun Aug 15 23:09:50 EDT 2021

STATUS

editing

proposed

#15 by Jon E. Schoenfield at Sun Aug 15 23:09:49 EDT 2021

NAME

Number of integer triples (x,y,z) satisfying |x|^3 + |y|^3 + |z|^3 = n, -n <= x,y,z <= n.

FORMULA

G.f.: ( 1 + 2*sum_Sum_{j>=1} x^(j^3) )^3.

STATUS

proposed

editing

#14 by Daniel Suteu at Sun Aug 15 15:46:37 EDT 2021

STATUS

editing

proposed

#13 by Daniel Suteu at Sun Aug 15 15:46:09 EDT 2021

FORMULA

a(n) = A175362(n) + 2*Sum_{k=1..floor(n^(1/3))} A175362(n - k^3). - Daniel Suteu, Aug 15 2021

PROG

(PARI) a(n, k=3) = if(n==0, return(1)); if(k <= 0, return(0)); if(k == 1, return(ispower(n, 3))); my(count = 0); for(v = 0, sqrtnint(n, 3), count += (2 - (v == 0))*if(k > 2, a(n - v^3, k-1), if(ispower(n - v^3, 3), 2 - (n - v^3 == 0), 0))); count; \\ Daniel Suteu, Aug 15 2021

STATUS

approved

editing

#12 by Joerg Arndt at Sat Apr 09 11:03:44 EDT 2016

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reviewed

approved

#11 by Michel Marcus at Sat Apr 09 03:11:50 EDT 2016

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proposed

reviewed

#10 by Michel Marcus at Sat Apr 09 03:11:44 EDT 2016

STATUS

editing

proposed

#9 by Michel Marcus at Sat Apr 09 03:11:40 EDT 2016

FORMULA

G.f. : ( 1+2*sum_{j>=1} x^(j^3) )^3.

STATUS

reviewed

editing

#8 by Joerg Arndt at Sat Apr 09 02:58:06 EDT 2016

STATUS

proposed

reviewed