OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k>=0} k*A191395(n,k).
G.f.: g(z) = 4*z^2/(1-2*z-z^2+2*z^3+(1-z^2)*sqrt(1-4*z^2))^2.
a(n) ~ 2^(n+3)/9 * (1-sqrt(2)/sqrt(Pi*n)). - Vaclav Kotesovec, Mar 21 2014
D-finite with recurrence n*a(n) -2*n*a(n-1) +6*(-n+2)*a(n-2) +12*(n-2)*a(n-3) +3*(3*n-8)*a(n-4) +6*(-3*n+8)*a(n-5) +4*(-n+3)*a(n-6) +8*(n-3)*a(n-7)=0. - R. J. Mathar, Oct 08 2016
EXAMPLE
a(4)=7 because in HHHH, HHUD, HUDH, UDHH, UDUD, and UUDD the sum of the heights of the base pyramids are 0, 1, 1, 1, 2, and 2, respectively.
MAPLE
g := 4*z^2/(1-2*z-z^2+2*z^3+(1-z^2)*sqrt(1-4*z^2))^2: gser := series(g, z = 0, 37): seq(coeff(gser, z, n), n = 0 .. 33);
MATHEMATICA
CoefficientList[Series[4*x^2/(1-2*x-x^2+2*x^3+(1-x^2)*Sqrt[1-4*x^2])^2, {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 21 2014 *)
PROG
(PARI) x='x+O('x^50); concat([0, 0], Vec(4*x^2/(1-2*x-x^2+2*x^3+(1-x^2)*sqrt(1-4*x^2))^2)) \\ G. C. Greubel, May 27 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Jun 04 2011
STATUS
approved