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Revision History for A340982

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A340982

Number of ways to write n as an ordered sum of 9 positive cubes.
(history; published version)

#9 by Alois P. Heinz at Tue Feb 02 20:05:12 EST 2021

STATUS

proposed

approved

#8 by Robert Israel at Tue Feb 02 19:01:40 EST 2021

STATUS

editing

proposed

#7 by Robert Israel at Tue Feb 02 19:01:34 EST 2021

LINKS

Robert Israel, <a href="/A340982/b340982.txt">Table of n, a(n) for n = 9..10000</a>

STATUS

approved

editing

#6 by Alois P. Heinz at Mon Feb 01 15:28:59 EST 2021

STATUS

editing

approved

#5 by Alois P. Heinz at Mon Feb 01 15:28:55 EST 2021

MAPLE

b:= proc(n, t) option remember;

`if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->

`if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))

end:

a:= n-> b(n, 9):

seq(a(n), n=9..94); # Alois P. Heinz, Feb 01 2021

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Mon Feb 01 11:05:49 EST 2021

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Mon Feb 01 10:49:40 EST 2021

CROSSREFS

Cf. A000578, A010057, A025462, A051344, A173682, A280618, A340977, A340978, A340979, A340980, A340981, A340983.

#2 by Ilya Gutkovskiy at Mon Feb 01 10:39:26 EST 2021

NAME

allocated for Ilya GutkovskiyNumber of ways to write n as an ordered sum of 9 positive cubes.

DATA

1, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 9, 0, 126, 0, 0, 0, 0, 72, 0, 126, 0, 0, 0, 0, 252, 0, 84, 0, 0, 0, 0, 504, 0, 36, 0, 0, 36, 0, 630, 0, 9, 0, 0, 252, 0, 504, 0, 10, 0, 0, 756, 0, 252, 0, 72, 0, 0, 1260, 0, 72, 0, 252, 84, 0, 1260, 0, 9, 0, 504, 504

OFFSET

9,8

LINKS

<a href="/index/Su#ssq">Index entries for sequences related to sums of cubes</a>

FORMULA

G.f.: (Sum_{k>=1} x^(k^3))^9.

MATHEMATICA

nmax = 94; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

CROSSREFS

Cf. A000578, A010057, A025462, A051344, A173682, A280618.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Feb 01 2021

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Feb 01 10:39:26 EST 2021

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved