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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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21
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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, 525453, 696078, 922108
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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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FORMULA
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EXAMPLE
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a(n) enumerates length n+2 sequences on {H,T} that end in HHT but do not contain the contiguous subsequence TTT.
a(3)=4 because we have: TTHHT, THHHT, HTHHT, HHHHT.
a(4)=6 because we have: TTHHHT, THTHHT, THHHHT, HTTHHT, HTHHHT, HHHHHT. - Geoffrey Critzer, Mar 01 2014
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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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MATHEMATICA
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nn=44; CoefficientList[Series[x(1+x+x^2)/(1-x-x^2+x^4), {x, 0, nn}], x] (* Geoffrey Critzer, Mar 01 2014 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 0, 1, 1]^(n-1)*[1; 2; 4; 6])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016
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CROSSREFS
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Related sequences are A000045 (HHH beats HHT, HTT beats TTH), A006498 (HHH beats HTH), A023434 (HHH beats HTT), A000930 (HHH beats THT, HTH beats HHT), A000931 (HHH beats TTH), A077868 (HHT beats HTH), A002620 (HHT beats HTT), A000012 (HHT beats THH), A004277 (HHT beats THT), A070550 (HTH beats HHH), 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), A128588 (HTT beats TTT).
Cf. A164315 (essentially the same sequence).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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