OFFSET
1,2
COMMENTS
From Ant King, Nov 01 2011: (Start)
lim(n->Infinity,a(2n+1)/a(2n))=1/5*(59+24*sqrt(6)).
lim(n->Infinity,a(2n)/a(2n-1))=1/5*(11+4*sqrt(6)).
(End)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Octagonal Triangular Number
Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).
FORMULA
For n odd, a(n+2) = 98*a(n+1)-a(n)+48; for n even, a(n+1) = 49*a(n)+24+10*(24*a(n)^2+24*a(n)+16)^0.5 - Richard Choulet, Oct 03 2007, Oct 09 2007
From Ant King, Nov 01 2011: (Start)
a(n) = a(n-1) + 98*a(n-2) - 98*a(n-3) - a(n-4) + a(n-5).
a(n) = 98*a(n-2) - a(n-4) + 48.
a(n) = 1/12*sqrt(3)(( sqrt(6)-(-1)^n)*(sqrt(3)+sqrt(2))^(2*n-1)-(sqrt(6)+(-1)^n)*(sqrt(3)-sqrt(2))^(2*n-1)-2*sqrt(3)).
a(n) = floor(1/12* sqrt(3)*(sqrt(6)-(-1)^n)*(sqrt(3)+sqrt(2))^(2*n-1)).
G.f.: x(1+5*x+49*x^2-5*x^3-2*x^4)/((1-x)(1-10*x+x^2)(1+10*x+x^2)).
(End)
MATHEMATICA
LinearRecurrence[{1, 98, -98, -1, 1}, {1, 6, 153, 638, 15041}, 18](* Ant King, Nov 01 2011 *)
PROG
(PARI) Vec((1+5*x+49*x^2-5*x^3-2*x^4)/((1-x)*(1-10*x+x^2)*(1+10*x+x^2))+O(x^99)) \\ Charles R Greathouse IV, Nov 01 2011
(Magma) I:=[1, 6, 153, 638, 15041]; [n le 5 select I[n] else Self(n-1)+98*Self(n-2)-98*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // Vincenzo Librandi, Dec 30 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Richard Choulet, Oct 03 2007
STATUS
approved