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 A357061 Number of edges in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts. 4
 4, 12, 36, 76, 132, 180, 292, 348, 516, 604, 804, 892, 1156, 1284, 1572, 1708, 2052, 2180, 2596, 2796, 3204, 3412, 3876, 4012, 4612, 4860, 5412, 5668, 6276, 6508, 7204, 7460, 8172, 8524, 9252, 9516, 10372, 10740, 11532, 11900, 12804, 13100, 14116, 14532, 15468, 15940, 16932, 17196, 18436 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The even values of n that yield squares with non-simple intersections are 32, 38, 44, 50, 54, 62, 76, 90, 98, ... . See A357058 and A357060 for images of the squares. LINKS Table of n, a(n) for n=0..48. FORMULA a(n) = A357058(n) + A357060(n) - 1 by Euler's formula. Conjecture: a(n) = 8*n^2 + 4 for squares that only contain simple intersections when cut by n internal squares. This is never the case for odd n >= 5. CROSSREFS Cf. A357058 (regions), A357060 (vertices), A355948, A355840, A355800, A357008 (triangle). Sequence in context: A095735 A020875 A307182 * A190072 A063810 A183931 Adjacent sequences: A357058 A357059 A357060 * A357062 A357063 A357064 KEYWORD nonn AUTHOR Scott R. Shannon, Sep 10 2022 STATUS approved

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Last modified September 30 21:59 EDT 2023. Contains 365812 sequences. (Running on oeis4.)