A126566 a(0)=1; a(1)=2; a(2)=5; a(3)=14; for n>3: a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3)-a(n-4).

1, 2, 5, 14, 43, 142, 495, 1794, 6681, 25346, 97357, 377038, 1468019, 5735758, 22460935, 88083586, 345754097, 1358000258, 5335796565, 20970349326, 82429113339, 324040664974, 1273932845663, 5008544929922, 19691924052361

Offset: 0

Author

Gary W. Adamson, Dec 28 2006

Keywords

• nonn

Comments

a(n) is also the first entry of the vector M^n*[1,0,0,0], where M is the type F_4 Cartan matrix [[2,-1,0,0]; [ -1,2,-2,0]; [0,-1,2,-1]; [0,0,-1,2]].

Crossrefs

Cf. A126569.

Programs

Mathematica

a = {1,2,5,14}; Do[AppendTo[a, 8*a[[ -1]]-20*a[[ -2]]+16*a[[ -3]]-a[[ -4]]],{24}]; a

Formula

G.f.: -(2*x-1)*(x^2-4*x+1)/(1-8*x+20*x^2-16*x^3+x^4). - R. J. Mathar, Nov 14 2007

Extensions

Edited and extended by Stefan Steinerberger, Aug 12 2007