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A101424
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Number of different cuboids with volume p^4 * q^n, where p,q are distinct prime numbers.
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4
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4, 9, 18, 28, 42, 57, 76, 96, 120, 145, 174, 204, 238, 273, 312, 352, 396, 441, 490, 540, 594, 649, 708, 768, 832, 897, 966, 1036, 1110, 1185, 1264, 1344, 1428, 1513, 1602, 1692, 1786, 1881, 1980, 2080, 2184, 2289, 2398, 2508, 2622, 2737, 2856, 2976, 3100
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OFFSET
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0,1
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COMMENTS
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Subsequence of A034836, which gives the number of cuboids for volume n.
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LINKS
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Table of n, a(n) for n=0..48.
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FORMULA
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a(n) = A034836(2^4*3^n) = A034836(3^4*2^n) = A034836(p^4*q^n) for p,q distinct primes.
From Colin Barker, Mar 28 2014: (Start)
The following is conjectured.
a(n) = (29 + 3*(-1)^n + 36*n + 10*n^2)/8.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: -(x+4)/((x+1)*(x-1)^3). (End)
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CROSSREFS
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Cf. A034836, A101423, A101425, A101426, A101427.
Sequence in context: A160172 A256536 A026412 * A301197 A008021 A228186
Adjacent sequences: A101421 A101422 A101423 * A101425 A101426 A101427
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KEYWORD
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nonn
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AUTHOR
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Anthony C Robin, Jan 17 2005
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EXTENSIONS
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Edited and extended by Ray Chandler, Dec 19 2008
a(0)=4 prepended and g.f. edited by Alois P. Heinz, Oct 05 2016
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STATUS
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approved
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