OFFSET
0,2
COMMENTS
a(n) = term (3,1) in M^n, M = the 3 X 3 matrix [1,1,2; 1,2,1; 1,1,1]. - Gary W. Adamson, Mar 12 2009
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 932
Index entries for linear recurrences with constant coefficients, signature (4,-1,-1).
FORMULA
MAPLE
spec:= [S, {S=Sequence(Union(Z, Z, Prod(Union(Sequence(Z), Z), Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
seq(coeff(series((1-x)/(1-4*x+x^2+x^3), x, n+1), x, n), n = 0..30); # G. C. Greubel, Oct 18 2019
MATHEMATICA
LinearRecurrence[{4, -1, -1}, {1, 3, 11}, 30] (* Vincenzo Librandi, Jun 22 2012 *)
PROG
(Magma) I:=[1, 3, 11]; [n le 3 select I[n] else 4*Self(n-1)-Self(n-2)-Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 22 2012
(PARI) my(x='x+O('x^30)); Vec((1-x)/(1-4*x+x^2+x^3)) \\ Altug Alkan, Sep 21 2018
(Sage)
def A052941_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1-x)/(1-4*x+x^2+x^3)).list()
A052941_list(30) # G. C. Greubel, Oct 18 2019
(GAP) a:=[1, 3, 11];; for n in [4..30] do a[n]:=4*a[n-1]-a[n-2]-a[n-3]; od; a; # G. C. Greubel, Oct 18 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 06 2000
STATUS
approved