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A073424

Triangle read by rows: T(m,n) = parity of 0^n + 0^m, n = 0,1,2,3 ..., m = 0,1,2,3, ... n.

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

0,1

COMMENTS

Parity of the sums of two powers of any even number.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150).

Franck Ramaharo, A generating polynomial for the pretzel knot, arXiv:1805.10680 [math.CO], 2018.

FORMULA

a(n) = parity [ (2k)^n + (2k)^m, n = 0, 1, 2, 3 ..., m = 0, 1, 2, 3, ... n ]

T(n,0) = 1- 0^n, T(n,k) = 0 for k>0. - Philippe Deléham, Feb 11 2012

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

EXAMPLE

a(3) = 1 because (2k)^2 + (2k)^0 = 4k^2 + 1 is odd.

Triangle begins :

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

MAPLE

0, seq(op([1, 0$n]), n=1..20); # Robert Israel, Mar 01 2016

MATHEMATICA

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 *)

CROSSREFS

Cf. A023531, A010054, A073423.

Sequence in context: A352824 A101309 A141474 * A135993 A334414 A285966

Adjacent sequences: A073421 A073422 A073423 * A073425 A073426 A073427

KEYWORD

easy,nonn,tabl

AUTHOR

Jeremy Gardiner, Jul 30 2002

STATUS

approved