|
Search: id:A006322
|
|
|
| A006322 |
|
4-dimensional analogue of centered polygonal numbers. |
|
+0
15
|
|
| 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; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Kekule numbers for certain benzenoids. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 18 2005
|
|
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).
|
|
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-x^2-3*x)/(x-1)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
|
|
CROSSREFS
|
Cf. A000217, A000330, A050446, A050447.
Sequence in context: A115293 A115004 A005338 this_sequence A055845 A034556 A121097
Adjacent sequences: A006319 A006320 A006321 this_sequence A006323 A006324 A006325
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Albert Rich (Albert_Rich(AT)msn.com)
|
|
|
Search completed in 0.002 seconds
|
