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Julia Crager, Felicia Flores, Timothy E. Goldberg, Lauren L. Rose, Daniel Rose-Levine, Darrion Thornburgh, and Raphael Walker, <a href="https://arxiv.org/abs/2212.05353">How many cards should you lay out in a game of EvenQuads? A detailed study of 2-caps in AG(2, n,2)</a>, arXiv:2212.05353 [math.CO], 2023.

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Julia Crager, Felicia Flores, Timothy E. Goldberg, Lauren L. Rose, Daniel Rose-Levine, Darrion Thornburgh, and Raphael Walker, <a href="https://arxiv.org/abs/2212.05353">How many cards should you lay out in a game of EvenQuads? A detailed study of 2-caps in AG(2, n)</a>, arXiv:2212.05353 [math.CO], 2023.

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The number of magic quads quad squares that can be formed using cards from Quads-2^n deck.

This sequence counts the number of magic quads quad squares that can be made using the Quads-2^n deck (a generalization of the standard Quads-64 deck). Here a magic quads quad square is defined as to be a 4-by-4 square of Quads cards so that each row, column, and diagonal forms a quad.

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Number The number of magic quads squares that can be formed using cards from Quads-2^n deck.

<a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (510,-86360,6217920,-205605888,3183575040,-22638755840,68451041280,-68719476736).

G.f.: 645120*x^4*(5+39920*x+70091776*x^2+11866341376*x^3) / ( (4*x-1) *(256*x-1) *(64*x-1) *(2*x-1) *(8*x-1) *(128*x-1) *(16*x-1) *(32*x-1) ). - R. J. Mathar, Jul 13 2023

A361613 := proc(n)

2^n*(2^n - 1)*(2^n - 2)*(2^n - 4)*(2^n - 8)*(10 + 85*(2^n - 16) + 43*(2^n - 16)*(2^n - 32) + (2^n - 16)*(2^n - 32)*(2^n - 64))

end proc:

seq(A361613(n), n=4..30) ; # R. J. Mathar, Jul 13 2023

nonn,easy

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