A215205 a(n) = (-1)^n * (A060819(n) + A060819(n+1)).

1, -2, 4, -4, 6, -8, 10, -9, 11, -14, 16, -14, 16, -20, 22, -19, 21, -26, 28, -24, 26, -32, 34, -29, 31, -38, 40, -34, 36, -44, 46, -39, 41, -50, 52, -44, 46, -56, 58, -49, 51, -62, 64, -54, 56, -68, 70, -59, 61, -74, 76, -64, 66, -80, 82, -69, 71, -86, 88, -74, 76, -92, 94, -79, 81, -98, 100, -84

Offset: 0

Author

Paul Curtz, Aug 06 2012

Keywords

• sign
• less
• easy

Comments

a(-1)=1=a(0).

a(n) - a(n-1) = b(n) = 0, -3, 6, -8, 10, -14, 18, -19, 20, -25, 30, -30, 30, -36, 42, -41, ... .

Missing terms in abs(a(n)):

PIII(n) = 0, 3, 5, 7, 12, 13, 15, 17, 18, 23, 25, 27, 30, 33, 35, 37, 42, ... . See A063241(n+1) and 6*A047222(n+1).

Quasipolynomial of order 4. - Charles R Greathouse IV, Aug 06 2012

Links

• Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,1,1,1,1).

Crossrefs

Cf. A016861, A016933, A016957, A016897.

Programs

Mathematica

a[n_] := Switch[Mod[n, 4], 0, 5n/4+1, 1, (-3n-1)/2, 2, 3n/2+1, 3, (-5n-1)/4]; Table[a[n], {n, 0, 67}] (* Jean-François Alcover, Nov 08 2012 *)

Formula

a(4*n) = 1+5*n, a(1+4*n) = -2-6*n, a(2+4*n) = 4+6*n, a(3+4*n) = -4-5*n.

a(n+4) - a(n) = period of length 4: repeat 5,-6, 6, -5.

a(n) = 2*a(n-4) + a(n-8).

G.f. ( -1+x-3*x^2-3*x^4+x^3+x^5-x^6 ) / ( (x-1)*(1+x)^2*(x^2+1)^2 ). - R. J. Mathar, Aug 07 2012

a(n) = (5+(2*n+1)*(11*(-1)^n-(-1)^((2*n-1+(-1)^n)/4))+(-1)^((6*n-1 +(-1)^n)/4))/16. - Luce ETIENNE, Jun 05 2015