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 A181395 Summed lengths of nonintersecting rook paths on a 4 X n board. 6
 3, 40, 284, 1912, 13132, 88608, 577727, 3659416, 22719964, 139088248, 842307548, 5055782456, 30119691570, 178296516264, 1049685801023, 6150604755800, 35890214413836, 208663068856540, 1209212316951436, 6987073893141896, 40267076160162015, 231512818498197668 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Paths are self-avoiding from one corner to the diagonally opposite corner. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 FORMULA Conjectured g.f.: x*(1 - x)*(3 - 29*x + 51*x^2 + 595*x^3 - 3879*x^4 + 9553*x^5 - 8366*x^6 - 8026*x^7 + 22931*x^8 - 13117*x^9 - 5593*x^10 + 7955*x^11 - 6118*x^12 + 6842*x^13 + 1884*x^14 - 6824*x^15 + 519*x^16 + 1991*x^17 - 206*x^18 - 230*x^19 + 13*x^20 + 9*x^21)/((1 - 8*x + 15*x^2 - 5*x^3 - 9*x^4 + 2*x^5 + x^6)^2*(1 - 4*x + 7*x^2 - 3*x^3 - 7*x^4 + 2*x^5 + x^6)^2). - Andrew Howroyd, Jan 06 2020 CROSSREFS Row 4 of A181399. Enumeration of these paths is A007786, related sequences A181394, A181396, A181397, A181398. Sequence in context: A013291 A013292 A278379 * A165395 A165386 A293501 Adjacent sequences:  A181392 A181393 A181394 * A181396 A181397 A181398 KEYWORD nonn AUTHOR David Scambler, Oct 17 2010 EXTENSIONS a(10)-a(13) from Alois P. Heinz, Dec 10 2011 Terms a(14) and beyond from Andrew Howroyd, Jan 06 2020 STATUS approved

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Last modified May 25 05:58 EDT 2022. Contains 354048 sequences. (Running on oeis4.)