OFFSET
0,1
COMMENTS
a(n) = sum of absolute values of terms in the (n+1)-th row of the triangle in A108561; - Reinhard Zumkeller, Jun 10 2005
a(n) = A078008(n+1) + 2*(1 + n mod 2). - Reinhard Zumkeller, Jun 10 2005
Essentially the same as A128209. - R. J. Mathar, Jun 14 2008
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1024
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).
FORMULA
G.f.: 2*(1-x-x^2)/((1-x^2)*(1-2*x)).
a(n) = a(n-1) + 2*a(n-2) - 2.
a(n) = 1 + Sum_{alpha=RootOf(-1+z+2*z^2)} (1 + 4*alpha)*alpha^(-1-n)/9.
a(2n) = 2*a(n-1)-2, a(2n+1) = 2*a(2n). - Lee Hae-hwang, Oct 11 2002
From Paul Barry, May 24 2004: (Start)
a(n) = A001045(n+1) + 1.
a(n) = (2^(n+1) - (-1)^(n+1))/3 + 1. (End)
E.g.f.: (2*exp(2*x) + 3*exp(x) + exp(-x))/3. - G. C. Greubel, Oct 21 2019
MAPLE
spec:= [S, {S=Union(Sequence(Union(Prod(Union(Z, Z), Z), Z)), Sequence(Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
seq((2^(n+1) +3 +(-1)^n)/3, n=0..40); # G. C. Greubel, Oct 21 2019
MATHEMATICA
LinearRecurrence[{2, 1, -2}, {2, 2, 4}, 40] (* G. C. Greubel, Oct 22 2019 *)
PROG
(Sage) [(2^(n+1) +3 +(-1)^n)/3 for n in (0..40)] # G. C. Greubel, Oct 21 2019
(PARI) vector(41, n, (2^n +3 -(-1)^n)/3 ) \\ G. C. Greubel, Oct 21 2019
(Magma) [(2^(n+1) +3 +(-1)^n)/3: n in [0..40]]; // G. C. Greubel, Oct 21 2019
(GAP) List([0..40], n-> (2^(n+1) +3 +(-1)^n)/3); # G. C. Greubel, Oct 21 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from James A. Sellers, Jun 05 2000
STATUS
approved