A129889 Write down n, then n*(n+1).

0, 0, 1, 2, 2, 6, 3, 12, 4, 20, 5, 30, 6, 42, 7, 56, 8, 72, 9, 90, 10, 110, 11, 132, 12, 156, 13, 182, 14, 210, 15, 240, 16, 272, 17, 306, 18, 342, 19, 380, 20, 420, 21, 462, 22, 506, 23, 552, 24, 600, 25, 650, 26, 702, 27, 756, 28, 812, 29, 870, 30, 930, 31, 992, 32, 1056, 33

Offset: 0

Author

N. J. A. Sloane, May 26 2007

Keywords

• nonn
• easy
• changed

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Cf. A124625.

Programs

Magma

[IsEven(n) select n/2 else (n^2-1)/4: n in [0..66]]; // Bruno Berselli, May 06 2011

Maple

f:=n-> if n mod 2 = 0 then n/2 else (n^2-1)/4; fi;

Mathematica

Flatten[Table[{n,n(n+1)},{n,0,40}]] (* Harvey P. Dale, Jun 21 2015 *)

Formula

From Bruno Berselli, May 06 2011: (Start)

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

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

a(n) = a(n-2) + A124625(n) for n>1. (End)