A199402 Binary XOR of 2^k - (-1)^k as k varies from 1 to n.

3, 0, 9, 6, 39, 24, 153, 102, 615, 408, 2457, 1638, 9831, 6552, 39321, 26214, 157287, 104856, 629145, 419430, 2516583, 1677720, 10066329, 6710886, 40265319, 26843544, 161061273, 107374182, 644245095, 429496728, 2576980377, 1717986918, 10307921511, 6871947672

Offset: 1

Author

Paul D. Hanna, Nov 05 2011

Keywords

• nonn

Comments

a(n) is divisible by 3; compare to A199403.

Examples

			a(2) = 2^1+1 XOR 2^2-1 = 3 XOR 3 = 0;
a(3) = 2^1+1 XOR 2^2-1 XOR 2^3+1 = 3 XOR 3 XOR 9 = 9;
a(4) = 2^1+1 XOR 2^2-1 XOR 2^3+1 XOR 2^4-1 = 3 XOR 3 XOR 9 XOR 15 = 6.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A199403.

Programs

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <-4|1|4>>^iquo(n-1, 2, 'r'). `if`(r=0, <<3, 9, 39>>, <<0, 6, 24>>))[1, 1]: seq(a(n), n=1..100);  # Alois P. Heinz, Nov 05 2011

PARI

{a(n)=if(n<0,0,bitxor(a(n-1),2^n-(-1)^n))}

Formula

G.f.: 3*(2*x^3-x^2+1)*x/(4*x^6-x^4-4*x^2+1). - Alois P. Heinz, Nov 05 2011