A168050 Hankel transform of A168049.

1, 1, 0, -1, -1, -2, -2, -3, -3, -4, -4, -5, -5, -6, -6, -7, -7, -8, -8, -9, -9, -10, -10, -11, -11, -12, -12, -13, -13, -14, -14, -15, -15, -16, -16, -17, -17, -18, -18, -19, -19, -20, -20, -21, -21, -22, -22, -23, -23, -24, -24, -25, -25, -26, -26, -27, -27

Offset: 0

Author

Paul Barry, Nov 17 2009

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Milan Janjić, Hessenberg Matrices and Integer Sequences, J. Int. Seq. 13 (2010) # 10.7.8.
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1)

Crossrefs

Cf. A168049.

Programs

Magma

[(-1)^n/4-(2*n-3)/4+Binomial(1,n)-Binomial(0,n): n in [0..80]]; // Vincenzo Librandi, Jul 08 2016

Mathematica

Join[{1,1,b=0},a=0;Table[c=b+2*a+n;a=b;b=c,{n,-1,60}]] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011 *)
CoefficientList[Series[(1 - 2 x^2 - x^3 + x^4)/((1 + x) (1 - x)^2), {x, 0, 100}], x] (* G. C. Greubel, Jul 07 2016 *)
Table[(-1)^n/4 - (2 n - 3)/4 + Binomial[1, n] - Binomial[0, n], {n, 0, 80}] (* Vincenzo Librandi, Jul 08 2016 *)
LinearRecurrence[{1,1,-1},{1,1,0,-1,-1},60] (* Harvey P. Dale, Dec 05 2018 *)

PARI

Vec((1-2*x^2-x^3+x^4)/((1+x)*(1-x)^2) + O(x^99)) \\ Altug Alkan, Jul 08 2016

Formula

G.f.: (1 - 2x^2 - x^3 + x^4)/((1+x)(1-x)^2).

a(n) = + 1*a(n-1) + 1*a(n-2) - 1*a(n-3). - Joerg Arndt, Apr 02 2011

a(n) = (-1)^n/4 -(2n-3)/4 + C(1,n) - C(0,n).

E.g.f.: (4*x + exp(-x) - (2*x - 3)*exp(x))/4. - Ilya Gutkovskiy, Jul 08 2016