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A006322
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4-dimensional analogue of centered polygonal numbers.
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15
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1, 8, 31, 85, 190, 371, 658, 1086, 1695, 2530, 3641, 5083, 6916, 9205, 12020, 15436, 19533, 24396, 30115, 36785, 44506, 53383, 63526, 75050, 88075, 102726, 119133, 137431, 157760, 180265, 205096, 232408, 262361, 295120, 330855
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Kekule numbers for certain benzenoids. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 18 2005
Partial sums give A006414. -- L. Edson Jeffery, Dec 13 2011.
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REFERENCES
| Manfred Goebel, Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials, Applicable Algebra in Engineering, Communication and Computing (AAECC), Volume 9, Issue 6 (1999), 559-573.
S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 166, Table 10.4/I/4).
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FORMULA
| a(n) = 5*C(n + 2, 4) + C(n + 1, 2) = (C(5*n+4, 4)-1)/5^3.
a(n) = [(n^5-(n-1)^5)-(n^3-(n-1)^3)]/24. - Xavier Acloque, Jan 14 2003
a(n) = Sum [ Sum ( 1 + Sum (5*n) ) ]. - Xavier Acloque, Jan 15 2003
G.f.:(1+3*x+x^2)/(1-x)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
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MATHEMATICA
| Table[5*Binomial[n+2, 4] + Binomial[n+1, 2], {n, 80}] (* From Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
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PROG
| (PARI) a(n)=n*(5*n^3-10*n^2+7*n-2)/24 \\ Charles R Greathouse IV, Dec 13 2011
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CROSSREFS
| Cf. A000217, A000330, A006414, A050446, A050447.
Sequence in context: A115293 A115004 A005338 * A055845 A034556 A121097
Adjacent sequences: A006319 A006320 A006321 * A006323 A006324 A006325
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KEYWORD
| nonn,easy
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AUTHOR
| Albert Rich (Albert_Rich(AT)msn.com)
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EXTENSIONS
| Simplified Maksym Voznyy's generating function, L. Edson Jeffery, Dec 13 2011.
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