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A084060
a(n) = 1/2 + (1-6*n)*(-1)^n/2.
1
1, 3, -5, 9, -11, 15, -17, 21, -23, 27, -29, 33, -35, 39, -41, 45, -47, 51, -53, 57, -59, 63, -65, 69, -71, 75, -77, 81, -83, 87, -89, 93, -95, 99, -101, 105, -107, 111, -113, 117, -119, 123, -125, 129, -131, 135, -137, 141, -143, 147, -149, 153, -155, 159, -161, 165, -167, 171, -173, 177, -179
OFFSET
0,2
COMMENTS
abs(a(n+1)) = A047270(n).
FORMULA
Unsigned version is sum of alternate terms of A032766 (numbers congruent to {0,1,3} mod 4): (1, 3, 4, 6, 7, 9, 10, 12, ...) such that a(n) = A032766(n-1) + A032766(n+1). - Gary W. Adamson, Sep 13 2007
G.f.: (1 + 4*x - 3*x^2 )/( (1-x)*(1+x)^2 ). - R. J. Mathar, Oct 25 2011
E.g.f.: (1+3*x)*cosh(x) - 3*x*sinh(x). - G. C. Greubel, Jan 03 2020
MAPLE
seq( (1 + (1-6*n)*(-1)^n)/2, n=0..60); # G. C. Greubel, Jan 03 2020
MATHEMATICA
Table[(1 + (1-6*n)*(-1)^n)/2, {n, 0, 60}] (* G. C. Greubel, Jan 03 2020 *)
LinearRecurrence[{-1, 1, 1}, {1, 3, -5}, 100] (* Harvey P. Dale, Mar 05 2023 *)
PROG
(Magma) [1/2+(1-6*n)*(-1)^n/2: n in [0..60]]; // Vincenzo Librandi, Oct 26 2011
(PARI) vector(61, n, (1 - (7-6*n)*(-1)^n)/2) \\ G. C. Greubel, Jan 03 2020
(Sage) [(1 + (1-6*n)*(-1)^n)/2 for n in (0..60)] # G. C. Greubel, Jan 03 2020
(GAP) List([0..60], n-> (1 + (1-6*n)*(-1)^n)/2) # G. C. Greubel, Jan 03 2020
CROSSREFS
Sequence in context: A191207 A285519 A047270 * A328574 A227157 A024896
KEYWORD
easy,sign
AUTHOR
Paul Barry, May 11 2003
STATUS
approved