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A192848
Molecular topological indices of the graph join C_n + C_n of cycle graphs.
1
12, 96, 300, 672, 1260, 2112, 3276, 4800, 6732, 9120, 12012, 15456, 19500, 24192, 29580, 35712, 42636, 50400, 59052, 68640, 79212, 90816, 103500, 117312, 132300, 148512, 165996, 184800, 204972, 226560, 249612, 274176, 300300, 328032, 357420, 388512, 421356, 456000, 492492, 530880, 571212, 613536
OFFSET
1,1
COMMENTS
Graph join C_n + C_n is defined and simple for n > 2; extended using recurrence for a(1) and a(2).
LINKS
Eric Weisstein's World of Mathematics, Cycle Graph.
Eric Weisstein's World of Mathematics, Graph Join.
Eric Weisstein's World of Mathematics, Molecular Topological Index.
FORMULA
a(n) = 4*n*(2+n)*(-1+2*n).
G.f.: 12*x*(1 + 4*x - x^2)/(1-x)^4. - Colin Barker, Aug 07 2012
E.g.f.: 4*x*(3 + 9*x + 2*x^2)*exp(x). - G. C. Greubel, Jan 05 2019
From Amiram Eldar, Apr 16 2022: (Start)
Sum_{n>=1} 1/a(n) = log(2)/5 - 3/80.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/20 - log(2)/10 - 1/80. (End)
MAPLE
A192848:=n->4*n*(2+n)*(-1+2*n): seq(A192848(n), n=1..70); # Wesley Ivan Hurt, Apr 10 2017
MATHEMATICA
Table[4n(2+n)(-1+2n), {n, 42}] (* Michael De Vlieger, Mar 09 2016 *)
Rest@CoefficientList[Series[ -12 x (x^2 - 4 x - 1)/(x - 1)^4, {x, 0, 42}], x] (* Michael De Vlieger, Mar 09 2016 *)
PROG
(PARI) vector(45, n, 4*n*(2+n)*(2*n-1)) \\ G. C. Greubel, Jan 05 2019
(Magma) [4*n*(2+n)*(2*n-1): n in [1..45]]; // G. C. Greubel, Jan 05 2019
(Sage) [4*n*(2+n)*(2*n-1) for n in (1..45)] # G. C. Greubel, Jan 05 2019
(GAP) List([1..45], n -> 4*n*(2+n)*(2*n-1)); # G. C. Greubel, Jan 05 2019
CROSSREFS
Sequence in context: A194782 A059154 A204630 * A229561 A341233 A120658
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 11 2011
EXTENSIONS
Name clarified by Eric W. Weisstein, Mar 09 2016
STATUS
approved