A174474 a(n) = (2*n^2 - 2*n - 3)/8 + 3*(-1)^n*(1-2*n)/8.

0, 0, -1, 3, 0, 8, 3, 15, 8, 24, 15, 35, 24, 48, 35, 63, 48, 80, 63, 99, 80, 120, 99, 143, 120, 168, 143, 195, 168, 224, 195, 255, 224, 288, 255, 323, 288, 360, 323, 399, 360, 440, 399, 483, 440, 528, 483, 575, 528, 624, 575

Offset: 0

Author

Paul Curtz, Nov 28 2010

Keywords

• sign
• easy

Comments

First differences are (-1)^n*A022998(n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Programs

Magma

[(2*n^2-2*n-3)/8+3*(-1)^n*(1-2*n)/8: n in [0..60]]; // Vincenzo Librandi, Aug 04 2011

Mathematica

LinearRecurrence[{1,2,-2,-1,1},{0,0,-1,3,0},60] (* Harvey P. Dale, Jun 01 2015 *)

Formula

Bisections: a(2n) = A067998(n). a(2n+1) = A005563(n).

a(2n) + a(2n+1) = A001105(n).

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

G.f.: x^2*(1 - 4*x + x^2) / ( (1+x)^2*(x-1)^3 ).