OFFSET
1,2
COMMENTS
Previous name was: Transform of A000217 without the initial 0 by the T_{0,0} transformation (see link).
Partial sums of A095263. - R. J. Mathar, Nov 04 2008
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 (4,-5,3,-1).
FORMULA
O.g.f: x/((1-x)*(1 -3*x +2*x^2 -x^3)).
a(n) = term (4,1) in the 4x4 matrix [3,1,0,0; -2,0,1,0; 1,0,0,0; 1,0,0,1]^(n). - Alois P. Heinz, Jul 24 2008
MAPLE
a:= n-> (<<3|1|0|0>, <-2|0|1|0>, <1|0|0|0>, <1|0|0|1>>^n)[4, 1]:
seq(a(n), n=1..50); # Alois P. Heinz, Jul 24 2008
MATHEMATICA
LinearRecurrence[{4, -5, 3, -1}, {1, 4, 11, 27}, 40] (* Harvey P. Dale, Nov 10 2014 *)
PROG
(Magma) I:=[1, 4, 11, 27]; [n le 4 select I[n] else 4*Self(n-1) -5*Self(n-2) +3*Self(n-3) -Self(n-4): n in [1..40]]; // G. C. Greubel, Apr 17 2021
(Sage)
def A137229_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x/((1-x)*(1-3*x+2*x^2-x^3)) ).list()
a=A137229_list(41); a[1:] # G. C. Greubel, Apr 17 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, Apr 05 2008
EXTENSIONS
New name using g.f., Joerg Arndt, Apr 18 2021
STATUS
approved