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A005920
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Tricapped prism numbers.
(Formerly M4611)
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5
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1, 9, 33, 82, 165, 291, 469, 708, 1017, 1405, 1881, 2454, 3133, 3927, 4845, 5896, 7089, 8433, 9937, 11610, 13461, 15499, 17733, 20172, 22825, 25701, 28809, 32158, 35757, 39615, 43741, 48144, 52833, 57817, 63105, 68706, 74629, 80883, 87477, 94420
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = (n+1)*A000326(n+1) - sum [i=0...n] A001477(i) = (n+1)*[(n+1)*(3*n+2)/2] - A000217(n) = (n+1)*(3*n^2+4n+2)/2 [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Apr 25 2010]
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| (1/2) * (3n^3 + 7n^2 + 6n + 2). - R. Stephan, Apr 20 2004
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MAPLE
| a:=n->(3*n^3+7*n^2+6*n+2)/2: seq(a(n), n=0..60);
A005920:=(1+5*z+3*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| CoefficientList[ Series[(1+5x+3x^2)/(1-x)^4, {x, 0, 39}], x] (* From Jean-François Alcover, Dec 02 2011, after Simon Plouffe *)
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CROSSREFS
| Cf. for recursive method [Ar(m) is the m-th term of a sequence in the OEIS] a(n) = n*Ar(n) - A000217(n-1) or a(n) = (n+1)*Ar(n+1) - A000217(n) or similar: A081436, A005945, A006003 and the terms T(2, n) or T(3, n) in the sequence A125860. [From Bruno Berselli (berselli.bruno(AT)yahoo.it), Apr 25 2010]
Sequence in context: A146823 A147027 A146256 * A020324 A146171 A146188
Adjacent sequences: A005917 A005918 A005919 * A005921 A005922 A005923
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 09 2004
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