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 A187172 T(n,k) is the number of n-step left-handed knight's tours (moves only out two, left one) on a k X k board summed over all starting positions. 7
 1, 4, 0, 9, 0, 0, 16, 8, 0, 0, 25, 24, 0, 0, 0, 36, 48, 16, 0, 0, 0, 49, 80, 60, 8, 0, 0, 0, 64, 120, 128, 48, 0, 0, 0, 0, 81, 168, 220, 176, 16, 0, 0, 0, 0, 100, 224, 336, 384, 136, 0, 0, 0, 0, 0, 121, 288, 476, 664, 456, 88, 0, 0, 0, 0, 0, 144, 360, 640, 1016, 1024, 496, 16, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts 1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 0 0 8 24 48 80 120 168 224 288 360 440 528 624 728 840 0 0 0 16 60 128 220 336 476 640 828 1040 1276 1536 1820 2128 0 0 0 8 48 176 384 664 1016 1440 1936 2504 3144 3856 4640 5496 0 0 0 0 16 136 456 1024 1804 2784 3964 5344 6924 8704 10684 12864 0 0 0 0 0 88 496 1440 3064 5344 8208 11640 15640 20208 25344 31048 0 0 0 0 0 16 368 1600 4284 8760 15104 23144 32764 43944 56684 70984 0 0 0 0 0 0 280 1784 5944 14072 27104 45288 68400 96048 128064 164424 0 0 0 0 0 0 88 1440 6828 19840 43668 80624 131576 196192 273592 363080 0 0 0 0 0 0 8 1088 7896 27984 70344 142816 250728 396808 580696 800584 LINKS R. H. Hardin, Table of n, a(n) for n = 1..310 FORMULA Empirical: T(1,k) = k^2; T(2,k) = 4*k^2 - 12*k + 8; T(3,k) = 12*k^2 - 64*k + 80 for k > 3; T(4,k) = 36*k^2 - 260*k + 440 for k > 5; T(5,k) = 100*k^2 - 920*k + 1984 for k > 7; T(6,k) = 284*k^2 - 3100*k + 7944 for k > 9; T(7,k) = 780*k^2 - 9880*k + 29384 for k > 11; T(8,k) = 2172*k^2 - 30972*k + 103944 for k > 13. EXAMPLE One of 98568 n=51 solutions for 16 X 16: 0 1 0 0 0 0 4 0 0 0 0 7 0 0 0 0 0 0 0 0 3 0 0 0 0 6 0 0 0 0 9 0 0 0 2 0 0 0 0 5 0 0 0 0 8 0 0 0 51 0 0 0 0 16 0 0 0 0 13 0 0 0 0 10 0 0 0 17 0 0 0 0 14 0 0 0 0 11 0 0 0 50 0 0 0 0 15 0 0 0 0 12 0 0 0 0 0 0 0 0 18 0 0 0 0 21 0 0 0 0 24 0 0 0 49 0 0 0 0 20 0 0 0 0 23 0 0 0 48 0 0 0 0 19 0 0 0 0 22 0 0 0 0 25 0 0 0 46 0 0 0 0 35 0 0 0 0 26 0 0 0 47 0 0 0 0 36 0 0 0 0 27 0 0 0 0 0 0 0 0 45 0 0 0 0 34 0 0 0 0 29 0 0 0 44 0 0 0 0 37 0 0 0 0 28 0 0 0 43 0 0 0 0 40 0 0 0 0 33 0 0 0 0 30 0 0 0 41 0 0 0 0 38 0 0 0 0 31 0 0 0 42 0 0 0 0 39 0 0 0 0 32 0 0 0 0 CROSSREFS Row 2 is A033996(n-2). Sequence in context: A260491 A013440 A013496 * A296570 A241667 A259258 Adjacent sequences: A187169 A187170 A187171 * A187173 A187174 A187175 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 06 2011 STATUS approved

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Last modified December 4 04:32 EST 2023. Contains 367541 sequences. (Running on oeis4.)