A142888 First differences of A142705.

3, -1, 13, -9, 29, -23, 51, -43, 79, -69, 113, -101, 153, -139, 199, -183, 251, -233, 309, -289, 373, -351, 443, -419, 519, -493, 601, -573, 689, -659, 783, -751, 883, -849, 989, -953, 1101, -1063, 1219, -1179, 1343, -1301, 1473, -1429, 1609, -1563, 1751

Offset: 1

Author

Paul Curtz, Sep 29 2008

Keywords

• sign
• easy

Comments

Also obtained from A135370 if adjacent pairs are swapped and if the sequence is then multiplied by (-1)^(n+1).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-1,2,2,-1,-1).

Crossrefs

Cf. A005843, A142705.

Programs

Mathematica

CoefficientList[Series[(3 + 2 x + 6 x^2 - x^4)/((1 + x)^3 (1 - x)^2), {x, 0, 60}], x] (* Vincenzo Librandi, May 25 2014 *)
LinearRecurrence[{-1,2,2,-1,-1},{3,-1,13,-9,29},50] (* Harvey P. Dale, Apr 02 2018 *)

PARI

Vec(x*(3+2*x+6*x^2-x^4)/((1+x)^3*(1-x)^2) + O(x^100)) \\ Colin Barker, Jan 26 2016

Formula

a(n) = A142705(n+1)-A142705(n).

a(n) = -a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5). - R. J. Mathar, Sep 12 2010

a(2n-1)+a(2n) = A005843(n).

G.f.: x(3+2x+6x^2-x^4)/((1+x)^3*(1-x)^2). - R. J. Mathar, Oct 24 2008, parenthesis added Sep 12 2010

From Colin Barker, Jan 26 2016: (Start)

a(n) = (5+3*(-1)^n+(10-6*(-1)^n)*n-6*(-1)^n*n^2)/8.

a(n) = (-3*n^2+2*n+4)/4 for n even.

a(n) = (3*n^2+8*n+1)/4 for n odd.

(End)

Extensions

Edited by R. J. Mathar, Oct 24 2008

More terms from Vincenzo Librandi, May 25 2014