OFFSET
0,2
COMMENTS
Equivalently, numbers k such that both k/2 and k+1 are squares. - Karl-Heinz Hofmann, Sep 20 2022
Equivalently, numbers k such that the k-dimensional volume and total (k-1)-dimensional volume are equal, with side length being a positive integer, for all regular polyhedra constructible in k dimensions. - Matt Moir, Jul 09 2024
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (35,-35,1).
FORMULA
a(0)=0, a(1)=8 and a(n) = 34*a(n-1) - a(n-2) + 16.
a(n) = (A056771(n) - 1)/2. - Max Alekseyev, Nov 13 2009
a(n) = sinh(2*n*arccosh(sqrt(2))^2) (n=0,1,2,3,...). - Artur Jasinski, Feb 10 2010
G.f.: -8*x*(x+1)/((x-1)*(x^2-34*x+1)). - Colin Barker, Oct 24 2012
MATHEMATICA
Table[Round[N[Sinh[2 n ArcCosh[Sqrt[2]]]^2, 100]], {n, 0, 20}] (* Artur Jasinski, Feb 10 2010 *)
LinearRecurrence[{35, -35, 1}, {0, 8, 288}, 30] (* Vincenzo Librandi, Dec 24 2018 *)
PROG
(Magma) I:=[0, 8, 288]; [n le 3 select I[n] else 35*Self(n-1)-35*Self(n-2)+ Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 24 2018
(Python)
A132592 = [0, 8]
print(A132592) # Karl-Heinz Hofmann, Sep 20 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohamed Bouhamida, Nov 14 2007
EXTENSIONS
More terms from Max Alekseyev, Nov 13 2009
STATUS
approved