A141620 First differences of A120070.

5, -3, 10, -3, -5, 17, -3, -5, -7, 26, -3, -5, -7, -9, 37, -3, -5, -7, -9, -11, 50, -3, -5, -7, -9, -11, -13, 65, -3, -5, -7, -9, -11, -13, -15, 82, -3, -5, -7, -9, -11, -13, -15, -17, 101, -3, -5, -7, -9, -11, -13, -15, -17, -19, 122, -3, -5, -7, -9, -11, -13, -15, -17, -19, -21

Offset: 0

Author

Paul Curtz, Aug 23 2008

Keywords

• sign

Crossrefs

Cf. A120070. Essentially the same as A133128.

Formula

a(n) = mix (from 2) n^2+1 (or A002522(n+2)), (ever from -3) successive -A005408.

a(n) = ((A^2+3*A-2*n)*(-A^2+A+2*(n+4))-(B^2+3*B-2*(n-1))*(-B^2+B+2*(n+3)))/4, where A = floor((sqrt(8*n+9)-1)/2) and B = floor((sqrt(8*(n-1)+9)-1)/2) = floor((sqrt(8*n+1)-1)/2). - Luce ETIENNE, May 31 2017