A319438 - OEIS

%I #13 Oct 05 2018 08:48:41

%S 1,1,-2,-80,-75,15545,15538,-5749256,-5749247,3481035145,3481035134,

%T -3134947341576,-3134947341563,3934241438357713,3934241438357698,

%U -6564474114274532912,-6564474114274532895,14056519977953450458097,14056519977953450458078

%N a(n) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 - 11^12 + 13^14 - ... + (up to n).

%C An alternating version of A318868.

%H Colin Barker, <a href="/A319438/b319438.txt">Table of n, a(n) for n = 1..350</a>

%F a(n) = n*(n mod 2)*(-1)^floor(n/2) + Sum_{i=1..floor(n/2)} (2*i - 1)^(2*i)*(-1)^(i - 1).

%e    a(1) = 1;

%e    a(2) = 1^2 = 1;

%e    a(3) = 1^2 - 3 = -2;

%e    a(4) = 1^2 - 3^4 = -80;

%e    a(5) = 1^2 - 3^4 + 5 = -75;

%e    a(6) = 1^2 - 3^4 + 5^6 = 15545;

%e    a(7) = 1^2 - 3^4 + 5^6 - 7 = 15538;

%e    a(8) = 1^2 - 3^4 + 5^6 - 7^8 = -5749256;

%e    a(9) = 1^2 - 3^4 + 5^6 - 7^8 + 9 = -5749247;

%e   a(10) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 = 3481035145;

%e   a(11) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 - 11 = 3481035134;

%e   a(12) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 - 11^12 = -3134947341576; etc .

%t Table[n*Mod[n, 2]*(-1)^(Floor[n/2]) + Sum[(2*i - 1)^(2*i)*(-1)^(i - 1), {i, Floor[n/2]}], {n, 30}]

%Y Cf. A093361, A228958, A305189, A318868.

%K sign,easy

%O 1,3

%A _Wesley Ivan Hurt_, Sep 18 2018