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A073424
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Triangle read by rows: T(m,n) = parity of 0^n + 0^m, n = 0,1,2,3 ..., m = 0,1,2,3, ... n.
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9
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0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
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OFFSET
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0,1
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COMMENTS
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Parity of the sums of two powers of any even number.
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LINKS
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FORMULA
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a(n) = parity [ (2k)^n + (2k)^m, n = 0, 1, 2, 3 ..., m = 0, 1, 2, 3, ... n ]
G.f.: Theta_2(0,sqrt(x))/(2*x^(1/8))-1, where Theta_2 is a Jacobi theta function. - Robert Israel, Mar 01 2016
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EXAMPLE
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a(3) = 1 because (2k)^2 + (2k)^0 = 4k^2 + 1 is odd.
Triangle begins :
0
1, 0
1, 0, 0
1, 0, 0, 0
1, 0, 0, 0, 0
1, 0, 0, 0, 0, 0
1, 0, 0, 0, 0, 0, 0
1, 0, 0, 0, 0, 0, 0, 0
1, 0, 0, 0, 0, 0, 0, 0, 0
1, 0, 0, 0, 0, 0, 0, 0, 0, 0 - Philippe Deléham, Feb 11 2012
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MAPLE
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MATHEMATICA
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Array[If[# == 1, {0}, PadRight[{1}, #]] &, 14] // Flatten (* or *)
Unprotect[Power]; Power[0, 0] = 1; Protect[Power]; Table[0^m + 0^n - 2 Boole[m == n == 0], {n, 0, 14}, {m, 0, n}] // Flatten (* Michael De Vlieger, Aug 22 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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