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Search: id:A100010
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| A100010 |
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Iterated hyperdiamond numbers, starting with 24-cell(2) = 24. Hyperdiamond numbers, figurate numbers based on the 4-dimensional 24-cell, have the formula 24-cell(n) = n^2*((3*n^2)-(4*n)+2). This sequence is the hyperdiamond number of the hyperdiamond number of ... of 2. |
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1
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| 2, 24, 941184, 2354066797535483525627904, 92129005371954174203312975604143711927454316666613485190398642854549697412939987602793680122937344
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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This need not start at 24-cell(2) = 24. For example, starting at a(0) = 3, which is not a hyperdiamond number, we have a(1) = 24-cell(3) = 3^2*((3*3^2)-(4*3)+2) = 153; and a(2) = 24-cell(24-cell(3)) = 24-cell(153) = 153^2*((3*153^2)-(4*153)+2) = 1629664353; and a(3) = 24-cell(24-cell(24-cell(3))) = 24-cell(1629664353) = 21159914972910583843562449776792301953.
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REFERENCES
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Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973.
J. V. Post, "Iterated Polygonal Numbers", preprint.
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LINKS
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Hyun Kwang Kim, On Regular Polytope Numbers.
J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000.
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FORMULA
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a(0) = 2; hyperdiamond numbers, figurate numbers based on the 4-dimensional 24-cell, have the formula 24-cell(n) = n^2*((3*n^2)-(4*n)+2). a(1) = 24-cell(2) = 24. a(2) = 24-cell(24-cell(2)) = 941184. For k>1, a(k+1) = 24-cell((a(k)).
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EXAMPLE
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a(2) = 941184 because a(0) = 2 is the seed for this instance of the more general recurrence, a(1) = 24-cell(2) = 2^2*((3*2^2)-(4*2)+2) = 24; a(2) = 24-cell(24-cell(2)) = 24-cell(24) = 24^2*((3*24^2)-(4*24)+2) = 941184.
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CROSSREFS
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Cf. A092181, A099053, A099179, A000332.
Adjacent sequences: A100007 A100008 A100009 this_sequence A100011 A100012 A100013
Sequence in context: A120122 A068943 A100815 this_sequence A045510 A065665 A036502
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 16 2004
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