A199396
Binary XOR of (3^k - 1)/2 as k varies from 1 to n.
Original entry on oeis.org
1, 5, 8, 32, 89, 309, 1392, 2464, 12241, 23685, 66936, 329856, 598377, 2972885, 4204000, 17321536, 47254689, 156943365, 737779176, 1276350496, 6369950073, 12290868597, 35051319632, 175157734688, 319624706161, 1569854375813, 2311734655064, 9333158201280, 25600877525257
Offset: 1
a(2) = (3^1-1)/2 XOR (3^2-1)/2 = 1 XOR 4 = 5;
a(3) = (3^1-1)/2 XOR (3^2-1)/2 XOR (3^3-1)/2 = 1 XOR 4 XOR 13 = 8;
a(4) = (3^1-1)/2 XOR (3^2-1)/2 XOR (3^3-1)/2 XOR (3^4-1)/2 = 1 XOR 4 XOR 13 XOR 40 = 32.
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FoldList[BitXor, Table[(3^n - 1)/2, {n, 1, 29}]] (* Vladimir Reshetnikov, Nov 02 2015 *)
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{a(n)=if(n<=0,0,bitxor(a(n-1),(3^n-1)/2))}
A199403
Binary XOR of (2^k - (-1)^k)/3 as k varies from 1 to n.
Original entry on oeis.org
1, 0, 3, 6, 13, 24, 51, 102, 205, 408, 819, 1638, 3277, 6552, 13107, 26214, 52429, 104856, 209715, 419430, 838861, 1677720, 3355443, 6710886, 13421773, 26843544, 53687091, 107374182, 214748365, 429496728, 858993459, 1717986918, 3435973837, 6871947672, 13743895347
Offset: 1
a(2) = (2^1+1)/3 XOR (2^2-1)/3 = 1 XOR 1 = 0;
a(3) = (2^1+1)/3 XOR (2^2-1)/3 XOR (2^3+1)/3 = 1 XOR 1 XOR 3 = 3;
a(4) = (2^1+1)/3 XOR (2^2-1)/3 XOR (2^3+1)/3 XOR (2^4-1)/3 = 1 XOR 1 XOR 3 XOR 5 = 6.
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a:= n-> (<<0|1|0|0|0>, <0|0|1|0|0>, <0|0|0|1|0>, <0|0|0|0|1>, <-2|1|0|0|2>>^n. <<0, 1, 0, 3, 6>>)[1, 1]: seq(a(n), n=1..60); # Alois P. Heinz, Nov 05 2011
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FoldList[BitXor, Table[(2^n - (-1)^n)/3, {n, 1, 20}]] (* Vladimir Reshetnikov, Nov 02 2015 *)
Table[(6*Cos[Pi n/2] + 2*Sin[Pi n/2] + 4*2^n - 5*(-1)^n - 5)/10, {n, 1, 20}] (* Vladimir Reshetnikov, Nov 02 2015 *)
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{a(n)=if(n<0,0,bitxor(a(n-1),((2^n-(-1)^n)/3)))}
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Vec(x*(3*x^2-2*x+1)/((x-1)*(x+1)*(2*x-1)*(x^2+1)) + O(x^100)) \\ Colin Barker, Nov 02 2015
Showing 1-2 of 2 results.