OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = (6^n+d(n)-sum(6^(k-1)*d(n-k),k=1..n))/2, where d(n) = central Delannoy number (A001850).
G.f.: (1-7*x+sqrt(1-6*x+x^2))/((2-12*x)*sqrt(1-6*x+x^2)).
Recurrence: (n^2+9*n+20)*a(n+5)-8*(3*n^2+23*n+44)*a(n+4)+2*(108*n^2+683*n+1089)*a(n+3)-2*(435*n^2+2159*n+2716)*a(n+2)+(1367*n^2+4917*n+4366)*a(n+1)-210*(n^2+3*n+2)*a(n)=0.
Conjecture: n*(2*n+3)*a(n) +2*(-12*n^2-15*n+22)*a(n-1) +(74*n^2+73*n-274)*a(n-2) -6*(2*n+5)*(n-2)*a(n-3)=0. - R. J. Mathar, Jul 24 2012
a(n) ~ (2+sqrt(2))/(2*sqrt(3*sqrt(2)-4)) * (3+2*sqrt(2))^n/sqrt(Pi*n). - Vaclav Kotesovec, Oct 20 2012
MATHEMATICA
CoefficientList[Series[(1-7x+Sqrt[1-6x+x^2])/((2-12x)Sqrt[1-6x+x^2]), {x, 0, 100}], x]
PROG
(PARI) x='x+O('x^50); Vec((1-7*x+sqrt(1-6*x+x^2))/((2-12*x)*sqrt(1-6*x+x^2))) \\ G. C. Greubel, Mar 26 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, May 17 2011
STATUS
approved