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URL: https://oeis.org/A142888

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A142888
First differences of A142705.
2
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
1,1
COMMENTS
Also obtained from A135370 if adjacent pairs are swapped and if the sequence is then multiplied by (-1)^(n+1).
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)
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 *)
PROG
(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
CROSSREFS
Sequence in context: A088814 A088729 A270968 * A331548 A068439 A133171
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Sep 29 2008
EXTENSIONS
Edited by R. J. Mathar, Oct 24 2008
More terms from Vincenzo Librandi, May 25 2014
STATUS
approved