The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A175368 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A175368

Number of integer 4-tuples (x,y,z,u) satisfying |x|^3 + |y|^3 + |z|^3 + |u|^3 = n, -n <= x,y,z,u <= n.
(history; published version)

#13 by Sean A. Irvine at Thu Aug 26 17:33:04 EDT 2021

STATUS

proposed

approved

#12 by Jon E. Schoenfield at Sun Aug 15 17:40:03 EDT 2021

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Sun Aug 15 17:40:01 EDT 2021

NAME

Number of integer 4-tuples (x,y,z,u) satisfying |x|^3 + |y|^3 + |z|^3 + |u|^3 = n, -n <= x,y,z,u <= n.

FORMULA

Conjectured g.f.: (1 + 2*Sum_{j>=1} x^(j^3))^4.

STATUS

proposed

editing

#10 by Daniel Suteu at Sun Aug 15 15:40:43 EDT 2021

STATUS

editing

proposed

#9 by Daniel Suteu at Sun Aug 15 15:40:41 EDT 2021

FORMULA

a(n) = A175365(n) + 2*Sum_{k=1..floor(n^(1/3))} A175365(n - k^3). - Daniel Suteu, Aug 15 2021

STATUS

proposed

editing

#8 by Michel Marcus at Sun Aug 15 05:55:06 EDT 2021

STATUS

editing

proposed

#7 by Michel Marcus at Sun Aug 15 05:55:02 EDT 2021

FORMULA

Conjecture: Conjectured g.f. : ( 1+2*sum_Sum_{j>=1} x^(j^3) )^4.

CROSSREFS

Cf. A000118 , A175362, A175365.

STATUS

proposed

editing

#6 by Daniel Suteu at Sun Aug 15 05:47:48 EDT 2021

STATUS

editing

proposed

#5 by Daniel Suteu at Sun Aug 15 05:46:43 EDT 2021

PROG

(PARI) a(n, k=4) = 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

#4 by Daniel Suteu at Sun Aug 15 05:44:59 EDT 2021

CROSSREFS

Cf. A175362, A175365, A175368.