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A093485
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(27*n^2 + 9*n + 2)/2.
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3
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1, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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)gmail.com), Oct 30 2006
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..10000
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FORMULA
| 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
| 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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PROG
| (MAGMA) [(27*n^2 + 9*n + 2)/2 : n in [0..50]]; // Vincenzo Librandi, Oct 08 2011
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CROSSREFS
| Cf. A000217, A000330, A003215, A005901, A006656.
Sequence in context: A183455 A183340 A195749 * A156967 A104047 A201781
Adjacent sequences: A093482 A093483 A093484 * A093486 A093487 A093488
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KEYWORD
| easy,nonn
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AUTHOR
| Michael Joseph Halm (hierogamous(AT)lycos.com), May 13 2004
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EXTENSIONS
| New definition from Ralf Stephan, Dec 01, 2004
Name corrected and initial term added by Arkadiusz Wesolowski, Aug 15 2011
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