|
|
A168076
|
|
Expansion of 1 - 3*(1-x-sqrt(1-2*x-3*x^2))/2.
|
|
3
|
|
|
1, 0, -3, -3, -6, -12, -27, -63, -153, -381, -969, -2505, -6564, -17394, -46533, -125505, -340902, -931716, -2560401, -7070337, -19609146, -54597852, -152556057, -427642677, -1202289669, -3389281245, -9578183391, -27130207503, -77009455428, -219023318406
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 0^n - 3*Sum_{k=0..floor((n-2)/2), C(n-2,2k)*A000108(k)}.
D-finite with recurrence: n*a(n) + (-2*n+3)*a(n-1) + 3*(-n+3)*a(n-2) = 0. - R. J. Mathar, Dec 03 2014
Recurrence (for n >= 3) follows from the differential equation (3*x^2+2*x-1)*y' - (3*x+1)*y = 3*x-1 satisfied by the g.f. - Robert Israel, May 13 2018
|
|
MAPLE
|
f:= gfun:-rectoproc({(3*n-3)*a(n)+(1+2*n)*a(n+1)+(-n-2)*a(n+2), a(0) = 1, a(1) = 0, a(2) = -3}, a(n), remember):
|
|
MATHEMATICA
|
CoefficientList[Series[1 - 3*(1 - x - Sqrt[1 - 2*x - 3*x^2])/2, {x, 0, 50}] , x] (* G. C. Greubel, Jul 09 2016 *)
|
|
PROG
|
(PARI) x='x+O('x^99); Vec(1-3*(1-x-(1-2*x-3*x^2)^(1/2))/2) \\ Altug Alkan, May 13 2018
(PARI) A168076(n)=!n-3*sum(k=0, n\2-1, binomial(n-2, 2*k)*binomial(2*k, k)/(k+1)) \\ M. F. Hasler, May 13 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|