OFFSET
1,3
COMMENTS
Triangular graphs are defined for n>=2; extended to n=1 using closed form.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
G. D. Birkhoff, A determinant formula for the number of ways of coloring a map, Ann. Math., 14:42-4. See 2nd polynomial p. 5.
Eric Weisstein's World of Mathematics, Molecular Topological Index.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = n*(n^2 - 1)*(n-2)^2.
a(n) = 24*A027800(n-3).
G.f.: 24*x^3*(4*x+1)/(x-1)^6. - Colin Barker, Aug 07 2012
a(n) = A245334(n+1,4), n > 2. - Reinhard Zumkeller, Aug 31 2014
E.g.f.: x^3*(4 + 6*x + x^2)*exp(x). - G. C. Greubel, Jan 05 2019
From Amiram Eldar, May 14 2022: (Start)
Sum_{n>=3} 1/a(n) = Pi^2/36 - 49/216.
Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/72 - 10*log(2)/9 + 145/216. (End)
MAPLE
[n*(n^2-1)*(n-2)^2$n=1..40]; # Muniru A Asiru, Jan 05 2019
MATHEMATICA
Table[n*(n^2-1)*(n-2)^2, {n, 1, 40}] (* G. C. Greubel, Jan 05 2019 *)
PROG
(Haskell)
a192849 n = if n < 3 then 0 else a245334 (n + 1) 4
-- Reinhard Zumkeller, Aug 31 2014
(PARI) vector(40, n, n*(n^2 -1)*(n-2)^2) \\ G. C. Greubel, Jan 05 2019
(Magma) [n*(n^2 -1)*(n-2)^2: n in [1..40]]; // G. C. Greubel, Jan 05 2019
(Sage) [n*(n^2 -1)*(n-2)^2 for n in (1..40)] # G. C. Greubel, Jan 05 2019
(GAP) List([1..40], n -> n*(n^2 -1)*(n-2)^2); # G. C. Greubel, Jan 05 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 11 2011
STATUS
approved