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 A358289 Generalized Gerrymander sequence: number of ordered ways to divide an n X n square into two connected regions, both of area n^2/2 if n is even, or of areas (n^2-1)/2 and (n^2+1)/2 if n is odd. 3
 0, 4, 16, 140, 2804, 161036, 27803749, 14314228378, 21838347160809, 99704315229167288, 1367135978051264146578, 56578717186086829451888706, 7065692298178203128922479762418, 2670113158846160742372913777087464324, 3052313665715695874527667027409186333152556 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Anthony J. Guttmann and Iwan Jensen, Table of n, a(n) for n = 1..17 Anthony J. Guttmann and Iwan Jensen, The gerrymander sequence, or A348456, arXiv:2211.14482 [math.CO], 2022. FORMULA a(2*n)/2 = A348456(n). EXAMPLE For n = 2, the square can be split vertically or horizontally, and then there are two ways to order the regions, so a(2) = 2*2 = 4. For n = 3 we must choose a connected region of area 4 with a connected complement of area 5. The possibilities are XXO XXX XXX XXO XOO OXO OOO OOO OOO 4 ways 8 ways 4 ways so a(3) = 16. CROSSREFS Cf. A348456. Sequence in context: A136651 A195899 A362143 * A156482 A335832 A173346 Adjacent sequences: A358286 A358287 A358288 * A358290 A358291 A358292 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 25 2022 STATUS approved

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Last modified June 9 15:05 EDT 2023. Contains 363181 sequences. (Running on oeis4.)