OFFSET
0,2
COMMENTS
abs(a(n+1)) = A047270(n).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (-1,1,1).
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
KEYWORD
easy,sign
AUTHOR
Paul Barry, May 11 2003
STATUS
approved