OFFSET
1,1
COMMENTS
Previous name was: Transform of A033999 by the T_{0,1} transformation (see link).
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Richard Choulet, Curtz-like transformation.
Index entries for linear recurrences with constant coefficients, signature (2,1,-1,1).
FORMULA
O.g.f: z*(2 -2*z +z^2 +z^3)/( (1+z)*(1-3*z+2*z^2-z^3) ).
a(n+4) = 2*a(n+3) + a(n+2) - a(n+1) + a(n).
From G. C. Greubel, Apr 11 2021: (Start)
a(n) = (1/7)*( 4*(-1)^n + Sum_{j=0..floor(n/2)} ( 10*binomial(n+j+2, 3*j+2) - 12*binomial(n+j+1, 3*j+2) + 11*binomial(n+j, 3*j+2) ) ). (End)
MAPLE
m:= 40;
S:= series( x*(2-2*x+x^2+x^3)/((1+x)*(1-3*x+2*x^2-x^3)), x, m+1);
seq(coeff(S, x, j), j = 1..m); # G. C. Greubel, Apr 11 2021
MATHEMATICA
LinearRecurrence[{2, 1, -1, 1}, {2, 2, 7, 15}, 30] (* Harvey P. Dale, Feb 02 2012 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (2-2*x+x^2+x^3)/((1+x)*(1-3*x+2*x^2-x^3)) )); // G. C. Greubel, Apr 11 2021
(Sage)
def A132749_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (2-2*x+x^2+x^3)/((1+x)*(1-3*x+2*x^2-x^3)) ).list()
A132749_list(40) # G. C. Greubel, Apr 11 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Apr 05 2008
EXTENSIONS
New name using g.f. from Joerg Arndt, Apr 19 2021
STATUS
approved