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Dmitry A. Zaitsev, A generalized neighborhood for cellular automata, Theoretical Computer Science, 2016, Volume 666, 1 March 2017, Pages 21-35; https://doi.org/10.1016/j.tcs.2016.11.002
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T(n,k) satisfies the cubic equation T(n,k)^3 + 3* A025581(n, k)*T(n,k) - 4*A105125(n,k) = 0. This is a problem similar to the one posed by François Viète (Vieta) mentioned in a comment on A025581. Here the problem is to determine for a rectangle (a, b), with a > b >= 1, from the given values for a^3 + b^3 and a - b the value of a + b. Here for nonnegative integers a = n and b = k. - Wolfdieter Lang, May 15 2015
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Row sums are A045943 = triangular matchstick numbers: 3n(n+1)/2. This was independently noted by myself and, without cross-reference, as a comment on A045943, by Jon Perry, Jan 15 2004. - Jonathan Vos Post, Nov 09 2007
T(n,k) satisfies the cubic equation T(n,k)^3 + 3* A025581(n, k)*T(n,k) - 4*A105125(n,k) = 0. This is a problem similar to the one posed by François Viète (Vieta) mentioned in a comment on A025581. Here the problem is to determine for a rectangle (a, b), with a > b >= 1, from the given values for a^3 + b^3 and a - b the value of a + b. Here for nonnegative integers a = n and b = k. - Wolfdieter Lang, May 15 2015
G.f.: x/(1-x)^2 + (1-x)^(-1)*Sum(j>=1, (1-j)*x^A000217(j)). The sum is related to Jacobi Theta functions. (End)
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