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A100010
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a(0) = 2 and a(n) = f(a(n-1)) where f(n) = n^2*(3*n^2-4*n+2).
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1
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OFFSET
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0,1
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COMMENTS
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Previous name was: 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.
The next term has 98 digits.
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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H. S. M. Coxeter, Regular Polytopes, 3rd ed. New York: Dover, 1973.
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LINKS
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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(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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PROG
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(PARI) f(n) = n^2*(3*n^2-4*n+2); \\ A092181
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CROSSREFS
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KEYWORD
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easy,nonn,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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