# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a361613 Showing 1-1 of 1 %I A361613 #22 Aug 09 2023 18:19:16 %S A361613 3225600,27398246400,58912149381120,35354354296504320, %T A361613 13112764372566835200,3994995853001760768000, %U A361613 1112834567045660389539840,296989774972633598731223040,77616116494664898347650252800,20075253208336550377420672204800,5165728566421154658646365736796160 %N A361613 The number of magic quad squares that can be formed using cards from Quads-2^n deck. %C A361613 This sequence is related to the game of EvenQuads: a deck of 64 cards with 3 attributes and 4 values in each attribute. Four cards form a quad when for every attribute, the values are either the same, all different, or half-half. %C A361613 This sequence counts the magic quad squares that can be made using the Quads-2^n deck (a generalization of the standard Quads-64 deck). Here a magic quad square is defined to be a 4-by-4 square of Quads cards so that each row, column, and diagonal forms a quad. %C A361613 a(n) is the number of 4-by-4 squares that can be made out of distinct numbers in the range from 0 to 2^n-1, so that each row, column, and diagonal bitwise XORs to 0. %H A361613 Julia Crager, Felicia Flores, Timothy E. Goldberg, Lauren L. Rose, Daniel Rose-Levine, Darrion Thornburgh, and Raphael Walker, How many cards should you lay out in a game of EvenQuads? A detailed study of 2-caps in AG(n,2), arXiv:2212.05353 [math.CO], 2023. %H A361613 Index entries for linear recurrences with constant coefficients, signature (510,-86360,6217920,-205605888,3183575040,-22638755840,68451041280,-68719476736). %F A361613 a(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)). %F A361613 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 %e A361613 An example of such a square is 0,1,2,3/4,5,6,7/8,9,10,11/12,13,14,15. %p A361613 A361613 := proc(n) %p A361613 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)) %p A361613 end proc: %p A361613 seq(A361613(n),n=4..30) ; # _R. J. Mathar_, Jul 13 2023 %t A361613 Table[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)), {n, 4, 15}] %Y A361613 Cf. A362874, A362963, A362964, A361495. %K A361613 nonn,easy %O A361613 4,1 %A A361613 _Tanya Khovanova_ and MIT PRIMES STEP senior group, May 11 2023 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE