A131723 a(2*n) = 1-n^2, a(2*n+1) = n*(n+1).

0, 2, -3, 6, -8, 12, -15, 20, -24, 30, -35, 42, -48, 56, -63, 72, -80, 90, -99, 110, -120, 132, -143, 156, -168, 182, -195, 210, -224, 240, -255, 272, -288, 306, -323, 342, -360, 380, -399, 420, -440, 462, -483, 506, -528, 552, -575, 600, -624, 650, -675

Offset: 0

Author

Paul Curtz, Sep 16 2007

Keywords

• sign
• easy

Comments

See A167683 for link to Hankel transform of A007325. Partial sum of signed version of A000096. [Paul Barry, Nov 09 2009]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (-2,0,2,1).

Crossrefs

Cf. A000096, A002378, A005563, A007325, A167683.

Programs

Magma

[-(-1)^n*(2*n^2+8*n+3-3*(-1)^n)/8: n in [0..50]]; // Vincenzo Librandi, Aug 10 2011

Maple

A131723:=n->-(-1)^n*floor((n+1)*(n+3)/4): seq(A131723(n), n=0..100); # Wesley Ivan Hurt, Jun 07 2016

Mathematica

Table[-(-1)^n*Floor[(n + 1)*(n + 3)/4], {n, 0, 100}] (* Wesley Ivan Hurt, Jun 07 2016 *)

Formula

From Paul Barry, Nov 09 2009: (Start)

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

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

From Wesley Ivan Hurt, Jun 07 2016: (Start)

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

a(n) = -(-1)^n*floor((n+1)*(n+3)/4).

a(2k) = - A005563(k), a(2k-1) = A002378(k) for k>0. (End)

Extensions

More terms from Vincenzo Librandi, Aug 10 2011