OFFSET
0,2
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 929
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
G.f.: (1+2*x-2*x^2)/((1+x)*(1-x)^2).
a(n) = -a(n-1) + n + 3, with a(0)=1.
a(n) = (3*(-1)^(n+1) + 2*n + 7)/4.
a(n) = A060762(n+1) - 1. - Filip Zaludek, Nov 19 2016
E.g.f.: ((5+x)*sinh(x) + (2+x)*cosh(x))/2. - G. C. Greubel, Oct 18 2019
MAPLE
spec := [S, {S=Prod(Union(Sequence(Z), Z, Z), Sequence(Prod(Z, Z)))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
seq((2*n+7-3*(-1)^n)/4, n=0..30); # G. C. Greubel, Oct 18 2019
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {1, 3, 2}, 80] (* Harvey P. Dale, Apr 10 2019 *)
PROG
(PARI) a(n)=([0, 1, 0; 0, 0, 1; -1, 1, 1]^n*[1; 3; 2])[1, 1] \\ Charles R Greathouse IV, Sep 02 2015
(Haskell)
a052938 n = a052938_list !! n
a052938_list = 1 : 3 : 2 : zipWith (-) [5..] a052938_list
-- Reinhard Zumkeller, Oct 06 2015
(Magma) [(2*n+7-3*(-1)^n)/4: n in [0..30]]; // G. C. Greubel, Oct 18 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 75); Coefficients(R!( (1 + 2*x - 2*x^2)/( (1+x)*(1-x)^2 ))); // Marius A. Burtea, Oct 18 2019
(Sage) [(2*n+7-3*(-1)^n)/4 for n in (0..30)] # G. C. Greubel, Oct 18 2019
(GAP) List([0..30], n-> (2*n+7-3*(-1)^n)/4); # 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