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A027800
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(n+1)*C(n+4,4).
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5
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1, 10, 45, 140, 350, 756, 1470, 2640, 4455, 7150, 11011, 16380, 23660, 33320, 45900, 62016, 82365, 107730, 138985, 177100, 223146, 278300, 343850, 421200, 511875, 617526, 739935, 881020, 1042840, 1227600, 1437656, 1675520
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Kekule numbers for certain benzenoids. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 19 2005
Equals binomial transform of [1, 9, 26, 34, 21, 5, 0, 0, 0,...]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 27 2008
a(n) equals the coefficient of x^4 of the characteristic polynomial of the (n+4)X(n+4) matrix with 2's along the main diagonal and 1's everywhere else (see Mathematica code below) [From John M. Campbell, Jul 08 2011]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-8.
S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p.233, # 9).
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LINKS
| M. Aganagic, A. Klemm and C. Vafa, Disk Instantons, Mirror Symmetry and the Duality Web
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FORMULA
| Number of 9-subsequences of [1, n] with just 4 contiguous pairs; g.f. (1+4x)/(1-x)^6
C(n+1, 1)*C(n+4, 4) - Zerinvary Lajos (zlaja(AT)freemail.hu), May 10 2005
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MAPLE
| a:=n->(n+1)^2*(n+2)*(n+3)*(n+4)/24: seq(a(n), n=0..36); (Deutsch)
a:=n->(sum((numbperm(n, 4)), j=4..n)):seq(a(n)/24, n=4..35); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 24 2008]
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MATHEMATICA
| Table[Coefficient[CharacteristicPolynomial[Array[KroneckerDelta[#1, #2] + 1 &, {n + 4, n + 4}], x], x^4], {n, 0, 40}] (* From John M. Campbell, Jul 08 2011*)
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CROSSREFS
| Partial sums of A002418.
Cf. A093562 ((5, 1) Pascal, column m=5).
Sequence in context: A022605 A179095 A037270 * A005714 A175705 A143671
Adjacent sequences: A027797 A027798 A027799 * A027801 A027802 A027803
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KEYWORD
| nonn
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AUTHOR
| thi ngoc dinh (via rkg(AT)cpsc.ucalgary.ca)
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