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 A165386 Number of slanted 3 X n (i=1..3) X (j=i..n+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, and 4 in the lower right corner. 2
 3, 40, 305, 1622, 6868, 25036, 82224, 250208, 718536, 1972132, 5220384, 13417184, 33652952, 82699012, 199729888, 475260768, 1116459752, 2593550148, 5965976992, 13605076608, 30787314104, 69191005796, 154539160288, 343241755840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS R. H. Hardin, Table of n, a(n) for n=2..58 FORMULA Empirical: a(n) = 12*a(n-1) - 63*a(n-2) + 190*a(n-3) - 363*a(n-4) + 456*a(n-5) - 377*a(n-6) + 198*a(n-7) - 60*a(n-8) + 8*a(n-9) for n>=13. Conjectures from Colin Barker, Feb 26 2018: (Start) G.f.: x^2*(3 + 4*x + 14*x^2 - 88*x^3 + 108*x^4 + 8*x^5 - 98*x^6 + 60*x^7 + 9*x^8 - 16*x^9 + 4*x^10) / ((1 - x)^6*(1 - 2*x)^3). a(n) = (-314880 + 315315*2^n - (139264+79785*2^n)*n + 5*(-5248+1323*2^n)*n^2 - 3280*n^3 - 160*n^4 - 16*n^5) / 240 for n>3. (End) EXAMPLE Some solutions for n=4: ...1.2.2.2.......1.1.2.2.......1.2.2.2.......1.1.3.2.......1.1.2.2.... .....2.2.2.3.......2.2.2.2.......4.4.4.4.......3.3.2.2.......3.3.2.4.. .......3.3.3.4.......3.2.2.4.......3.4.4.4.......3.3.4.4.......3.4.4.4 ------ ...1.1.1.2.......1.1.2.2.......1.1.1.2.......1.1.1.2.......1.1.2.2.... .....1.3.2.2.......1.3.2.4.......3.3.3.3.......1.3.2.4.......3.3.3.3.. .......3.2.2.4.......3.4.4.4.......3.3.3.4.......3.4.4.4.......3.3.3.4 ------ ...1.2.2.2.......1.1.3.2.......1.1.2.2.......1.1.1.2.......1.1.2.2.... .....3.3.3.3.......3.3.3.3.......1.1.1.1.......2.2.2.2.......1.3.2.4.. .......3.3.4.4.......3.3.4.4.......3.3.3.4.......3.2.2.4.......3.3.4.4 CROSSREFS Sequence in context: A278379 A181395 A165395 * A293501 A002700 A220639 Adjacent sequences:  A165383 A165384 A165385 * A165387 A165388 A165389 KEYWORD nonn AUTHOR R. H. Hardin, Sep 17 2009 STATUS approved

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Last modified January 19 06:18 EST 2022. Contains 350464 sequences. (Running on oeis4.)