1,2

Three-dimensional cage assemblies. (See Chapter 61, "Hyperspace Prisons", of C. A. Pickover's book "Wonders of Numbers" for full explanation of "cage numbers.")

For n>=0 the number of 3 X 3 matrices with nonnegative integer entries such that every row sum equals n is a(n+1). - Sharon Sela (sharonsela(AT)hotmail.com), May 14 2002

C. A. Pickover. "Wonders of Numbers: Adventures in Mathematics, Mind and Meaning." Oxford University Press. New York, NY, 2001.

Harry J. Smith, Table of n, a(n) for n=1,...,1000

C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Also a(n) = Sum[Sum[i*j^3, {i, 1, n}], {j, 1, n}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 25 2006

for n from 1 to 100 do printf(`%d, `, ((n^3)*(n + 1)^3)/8) od:

[seq(binomial(n+2, n)^3, n=0..50)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2006

a:=n->sum(sum(sum(j*k*m, j=1..n), k=1..n), m=1..n): seq(a(n), n=1..28); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 11 2007

a:=n->sum(k^3*sum(k, k=0..n), k=0..n):seq(a(n), n=1...28); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 01 2008

a:=n->sum(k^3*sum(k, k=0..n), k=0..n):seq(a(n), n=1...28); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 09 2008]

lst={}; Do[s0=n^3; s1=(n+1)^3; AppendTo[lst, (s1*s0)/8], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 19 2009]

(PARI) { for (n=1, 1000, write("b059827.txt", n, " ", (n*(n + 1)/2)^3); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 29 2009]

Cf. A070307, A001844.

Sequence in context: A033544 A125111 A016767 this_sequence A117688 A107054 A160441

Adjacent sequences: A059824 A059825 A059826 this_sequence A059828 A059829 A059830

nonn,easy

Jason Earls (zevi_35711(AT)yahoo.com), Feb 24 2001

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 26 2001