login
Abs(*+-) n Sequence.
0

%I #6 Jan 21 2019 19:01:55

%S 1,2,5,1,15,9,16,65,56,66,166,154,167,336,321,337,593,575,594,955,934,

%T 956,1440,1416,1441,2066,2039,2067,2851,2821,2852,3813,3780,3814,4970,

%U 4934,4971,6340,6301,6341,7941,7899,7942,9791,9746,9792,11908,11860

%N Abs(*+-) n Sequence.

%F ABS(1+2*3-4+...+(n-2)*(n-1)-n)

%F a(3*s) = abs[4 + 3*A000217(s) - 2*s - 9*A000217(s - 1) - 9*A000330(s - 1)] = abs[4 + 5s/2 + 3s^2/2 - 3s^3], s = 1, 2, 3... a(3*s - 1) = abs[4 + 3*A000217(s) - 5*s - 9*A000217(s - 1) - 9*A000330(s - 1)] = abs[4 - s/2 + 3s^2/2 - 3s^3], s = 1, 2, 3.. - _R. J. Mathar_, Jan 25 2007

%e a(1)=1

%e a(2)=1*2

%e a(3)=1*2+3

%e a(4)=1*2+3-4

%e a(5)=1*2+3-4*5

%e a(6)=1*2+3-4*5+6

%e a(7)=1*2+3-4*5+6-7

%e a(8)=1*2+3-4*5+6-7*8

%t s={1,2};b=2;Do[b=b+Switch[Mod[n,3],0,Plus[n],1,-n,2,-(n-1)^2];AppendTo[s,Abs[b]],{n,3,50}];s - _Zak Seidov_, Jul 30 2006

%K nonn

%O 1,2

%A _Jorge Coveiro_, Jul 27 2006

%E Corrected and extended by _Zak Seidov_, Jul 30 2006