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A059977
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Binomial(n+2,2)^4.
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3
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1, 81, 1296, 10000, 50625, 194481, 614656, 1679616, 4100625, 9150625, 18974736, 37015056, 68574961, 121550625, 207360000, 342102016, 547981281, 855036081, 1303210000, 1944810000, 2847396321, 4097152081, 5802782976, 8100000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Number of 4-dimensional cage assemblies.
See Chap. 61, "Hyperspace Prisons", of C. Pickover's book "Wonders of Numbers" for full explanation of "cage numbers."
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REFERENCES
| Clifford Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, 2001, p. 325.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
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FORMULA
| L(n) = ((n^m)(n + 1)^m)/(2^m) where m is the dimension, which in this case is 4.
O.g.f.: -(1+72*x+603*x^2+1168*x^3+603*x^4+72*x^5+x^6)/(-1+x)^9. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 31 2008
a(n) = A000217(n+1)^4. - R. J. Mathar, Dec 13 2011
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MAPLE
| with (combinat):seq(mul(stirling2(n+1, n), k=1..4), n=1..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2007
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MATHEMATICA
| m = 4; Table[ ( (n^m)(n + 1)^m )/(2^m), {n, 1, 30} ]
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PROG
| (Other) SAGE:[stirling_number2(n+1, n)^4for n in xrange(1, 25)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 14 2009]
(PARI) { for (n=0, 1000, write("b059977.txt", n, " ", ((n + 1)*(n + 2)/2)^4); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 30 2009]
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CROSSREFS
| Cf. A059827, A059860.
Sequence in context: A205729 A183807 A016768 * A116205 A110921 A203650
Adjacent sequences: A059974 A059975 A059976 * A059978 A059979 A059980
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 06 2001
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EXTENSIONS
| Better definition from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 23 2006
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