login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A107915 a(n) = binomial(n+4,4)*binomial(n+5,4)*binomial(n+6,4)/75. 7
1, 35, 490, 4116, 24696, 116424, 457380, 1557270, 4723719, 13026013, 33157124, 78835120, 176729280, 376375104, 766192176, 1498581756, 2828205765, 5168991135, 9177226366, 15870391460, 26794167400, 44253495000, 71627692500, 113794603650, 177694650315 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Kekulé numbers for certain benzenoids.
Partial sums of A107917. - Peter Bala, Sep 21 2007
REFERENCES
S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229).
LINKS
Stefan Felsner, Eric Fusy, Marc Noy, and David Orden, Bijections for Baxter families and related objects, J. Combin. Theory Ser. A, 118(3):993-1020, 2011.
FORMULA
a(n) = C(n,n-2)*C(n+1,n-3)*C(n+2,n-4)/(5*3!), n>=4. - Zerinvary Lajos, May 29 2007
a(n-3) = (1/144) * Sum_{1 <= x_1, x_2, x_3 <= n} x_1*x_2*x_3*(det V(x_1,x_2,x_3))^2 = 1/144*sum {1 <= i,j,k <= n} i*j*k*((i-j)(i-k)(j-k))^2, where V(x_1,x_2,x_3) is the Vandermonde matrix of order 3. - Peter Bala, Sep 21 2007
G.f.: -(x^6+22*x^5+113*x^4+190*x^3+113*x^2+22*x+1)/(x-1)^13. - Colin Barker, Jun 06 2012
From Amiram Eldar, May 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 25200*Pi^2 - 248713.
Sum_{n>=0} (-1)^n/a(n) = 376003 - 430080*log(2) - 64800*zeta(3). (End)
MAPLE
a:=n->(1/75)*binomial(n+4, 4)*binomial(n+5, 4)*binomial(n+6, 4): seq(a(n), n=0..27);
seq(binomial(n, n-2)*binomial(n+1, n-3)*binomial(n+2, n-4)/(5*3!), n=4..22); # Zerinvary Lajos, May 29 2007
MATHEMATICA
a[n_] := Binomial[n + 4, 4] * Binomial[n + 5, 4] * Binomial[n + 6, 4]/75; Array[a, 25, 0] (* Amiram Eldar, May 29 2022 *)
CROSSREFS
Sequence in context: A298946 A219582 A177079 * A219370 A278674 A219468
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 12 2005
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)