OFFSET
0,2
COMMENTS
a(n) is also the number of acyclic orientations of the complete bipartite graph K_{6,n}. - Vincent Pilaud, Sep 16 2020
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1179
Index entries for linear recurrences with constant coefficients, signature (27,-295,1665,-5104,8028,-5040).
FORMULA
a(n) = 720*7^n - 1800*6^n + 1560*5^n - 540*4^n + 62*3^n - 2^n.
From Colin Barker, Oct 14 2020: (Start)
G.f.: (1 - x)^2*(1 + 39*x + 38*x^2 - 120*x^3) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)).
a(n) = 27*a(n-1) - 295*a(n-2) + 1665*a(n-3) - 5104*a(n-4) + 8028*a(n-5) - 5040*a(n-6) for n>5. (End)
E.g.f.: exp(2*x)*(720*exp(5*x) - 1800*exp(4*x) + 1560*exp(3*x) - 540*exp(2*x) + 62*exp(x) - 1). - Stefano Spezia, May 18 2024
MATHEMATICA
Table[720*7^n - 1800*6^n + 1560*5^n - 540*4^n + 62*3^n - 2^n , {n, 0, 18}] (* Indranil Ghosh, Mar 17 2017 *)
PROG
(PARI) a(n) = 720*7^n - 1800*6^n + 1560*5^n - 540*4^n + 62*3^n - 2^n; \\ Indranil Ghosh, Mar 17 2017
(PARI) Vec((1 - x)^2*(1 + 39*x + 38*x^2 - 120*x^3) / ((1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)) + O(x^20)) \\ Colin Barker, Oct 14 2020
(Python) def A283812(n): return 720*7**n - 1800*6**n + 1560*5**n - 540*4**n + 62*3**n - 2**n # Indranil Ghosh, Mar 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 17 2017
STATUS
approved