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A171861
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Expansion of x*(1+x+x^2) / ( (x-1)*(x^3+x^2-1) ).
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19
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1, 2, 4, 6, 9, 13, 18, 25, 34, 46, 62, 83, 111, 148, 197, 262, 348, 462, 613, 813, 1078, 1429, 1894, 2510, 3326, 4407, 5839, 7736, 10249, 13578, 17988, 23830, 31569, 41821, 55402, 73393, 97226, 128798, 170622, 226027, 299423, 396652
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OFFSET
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1,2
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COMMENTS
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Number of wins in Penney's game if the two players start HHT and TTT and HHT beats TTT.
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LINKS
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Table of n, a(n) for n=1..42.
Wikipedia, Penney's game
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FORMULA
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a(n)= +a(n-1) +a(n-2) -a(n-4) = A000931(n+10)-3 = A134816(n+6)-3 = A078027(n+12)-3 .
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MAPLE
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A171861 := proc(n) option remember; if n <=4 then op(n, [1, 2, 4, 6]); else procname(n-1)+procname(n-2)-procname(n-4) ; end if; end proc:
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CROSSREFS
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Related sequences are A000045 (HHH beats HHT), A006498 (HHH beats HTH), A023434 (HHH beats HTT), A000930 (HHH beats THT), A000931 (HHH beats TTH), A077868 (HHT beats HTH), A002620 (HHT beats HTT), A000012 (HHT beats THH), A004277 (HHT beats THT), A070550 (HTH beats HHH), A000930 (HTH beats HHT), A000027 (HTH beats HTT), A097333 (HTH beats THH), A040000 (HTH beats TTH), A068921 (HTH beats TTT), A054405 (HTT beats HHH), A008619 (HTT beats HHT), A038718 (HTT beats THT), A000045 (HTT beats TTH), A128588 (HTT beats TTT).
Sequence in context: A088575 A177189 A026906 * A039900 A039902 A081659
Adjacent sequences: A171858 A171859 A171860 * A171862 A171863 A171864
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KEYWORD
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easy,nonn
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AUTHOR
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Ed Pegg Jr, Oct 16 2010
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STATUS
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approved
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