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Search: id:A093485
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| A093485 |
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(1/2) (27n^2 + 63n + 38). |
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+0
3
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| 19, 64, 136, 235, 361, 514, 694, 901, 1135, 1396, 1684, 1999, 2341, 2710, 3106, 3529, 3979, 4456, 4960, 5491, 6049, 6634, 7246, 7885, 8551, 9244, 9964, 10711, 11485, 12286, 13114, 13969, 14851, 15760, 16696, 17659, 18649, 19666, 20710, 21781
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OFFSET
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0,1
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COMMENT
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Dodecahedral gnomic numbers: first differences of dodecahedral numbers.
The sequence is related to other gnomons of polyhedra, known by other more familiar names: triangular (tetrahedral gnomic), hex (cubic gnomic), square pyramidal numbers (octohedral gnomic)
A124388 = first differences; second differences = 27. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Oct 30 2006
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FORMULA
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a(n) = (n+1)*(3*(n+1)-1)*(3*(n+1)-2)/2-n*(3*n-1)*(3*n-2)/2
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EXAMPLE
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a(1) = 19 because (1+1)*(3*(1+1)-1)*(3*(1+1)-2)/2-1*(3*1-1)*(3*1-2)/2 = 2*(6-1)*(6-2)/2 - 1*(3-1)*(3-2)/2 = 20-1 = 19
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CROSSREFS
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Cf. A000217, A000330, A003215, A005901, A006656.
Sequence in context: A092327 A139498 A106087 this_sequence A142404 A139927 A044157
Adjacent sequences: A093482 A093483 A093484 this_sequence A093486 A093487 A093488
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KEYWORD
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easy,nonn
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AUTHOR
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Michael Joseph Halm (hierogamous(AT)lycos.com), May 13 2004
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EXTENSIONS
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New definition from Ralf Stephan, Dec 01, 2004
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