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A087328
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Independence numbers for KT_3 knight on hexagonal board.
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3
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1, 3, 4, 4, 9, 12, 15, 16, 22, 27, 31, 36, 43, 51, 58, 64, 75, 83, 93, 100, 112, 123, 133, 144, 157, 171, 184, 196, 213, 227, 243, 256, 274, 291, 307, 324, 343, 363, 382, 400, 423, 443, 465, 484, 508, 531, 553, 576, 601, 627, 652, 676, 705, 731, 759, 784, 814
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OFFSET
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1,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1,0,-1,2,0,-2,1).
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FORMULA
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a(n) = ceiling(n^2/4) if n == 0, 1, 4, 8, 11 (mod 12), ceiling(n^2/4) + 1 if n == 3, 9 (mod 12) and ceiling(n^2/4) + 2 if n == 2, 5, 6, 7, 10 (mod 12) and n != 6.
G.f.: x*(1+x-2*x^2-2*x^3+6*x^4-x^5-4*x^6+x^7+3*x^8-x^9+x^11-2*x^12+2*x^14-x^15) / ((1-x)^3*(1+x)*(1+x^2)*(1-x^2+x^4)). - Colin Barker, Feb 02 2016
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PROG
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(PARI) Vec(x*(1+x-2*x^2-2*x^3+6*x^4-x^5-4*x^6+x^7+3*x^8-x^9+x^11-2*x^12+2*x^14-x^15)/((1-x)^3*(1+x)*(1+x^2)*(1-x^2+x^4)) + O(x^100)) \\ Colin Barker, Feb 02 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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