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 A372198 The number of ways of 2-coloring the diagram for the n-th centered square number up to rotation and reflection of the square. 0
 2, 12, 1236, 4215840, 274888655360, 288230395747516416, 4835703278617945885900800, 1298074214633711825063417305104384, 5575186299632655786027352001453113896599552, 383123885216472214589587083913232677066440014825521152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The centered square numbers are given by A001844. The diagram for the n-th centered square number is the set of integer pairs (x,y) such that |x| + |y| <= n. LINKS Table of n, a(n) for n=0..9. Eric Weisstein's World of Mathematics, Centered Square Number. FORMULA a(n) = 1/8*(2^A001844(n) + 2*2^((n+1)^2) + 2*2^A000124(n) + 2^A002061(n+1) + 2*2^A014848(n+1)). EXAMPLE For n=1 the a(1) = 12 inequivalent colorings are: 0 1 1 0 1 1 0 0 0, 0 0 0, 1 0 0, 1 0 1, 1 0 1, and 1 0 1, 0 0 0 0 0 1 along with 1 0 0 1 0 0 1 1 1, 1 1 1, 0 1 1, 0 1 0, 0 1 0, and 0 1 0. 1 1 1 1 1 0 For n = 2, the corresponding diagram has A001844(2) = 13 boxes and a(2) = 1236 inequivalent colorings. For instance, the following two colorings are considered equivalent, because one can be transformed to the other by a reflection. +---+ +---+ | 1 | | 1 | +---+---+---+ +---+---+---+ | 1 | 1 | | | 1 | | 1 | +---+---+---+---+---+ +---+---+---+---+---+ | 1 | | | 1 | | | 1 | 1 | | | 1 | +---+---+---+---+---+ +---+---+---+---+---+ | 1 | | | | | 1 | | +---+---+---+ +---+---+---+ | 1 | | | +---+ +---+ CROSSREFS Cf. A000124, A001844, A002061, A014848. Sequence in context: A177361 A138486 A022482 * A081701 A069714 A176391 Adjacent sequences: A372193 A372194 A372195 * A372199 A372200 A372201 KEYWORD nonn AUTHOR Peter Kagey, Apr 21 2024 STATUS approved

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Last modified June 21 03:10 EDT 2024. Contains 373535 sequences. (Running on oeis4.)