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A164480
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Number of binary strings of length n with no substrings equal to 0001, 0110 or 1100.
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1
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1, 2, 4, 8, 13, 21, 34, 55, 88, 142, 229, 370, 598, 967, 1564, 2530, 4093, 6622, 10714, 17335, 28048, 45382, 73429, 118810, 192238, 311047, 503284, 814330, 1317613, 2131942, 3449554, 5581495, 9031048, 14612542, 23643589, 38256130, 61899718, 100155847
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 500 terms from R. H. Hardin)
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
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FORMULA
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From Colin Barker, Oct 27 2017: (Start)
G.f.: -(x^8+x^5+x^4-x^3-1)/((x-1)*(x^2+x-1)).
a(n) = 2*a(n-1) - a(n-3) for n>6.
(End)
a(n) = 3*Lucas(n-1) + 1 for n >= 6. - Greg Dresden, Oct 10 2020
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PROG
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(PARI) Vec(-(x^8+x^5+x^4-x^3-1)/((x-1)*(x^2+x-1)) + O(x^60)) \\ Colin Barker, Oct 27 2017
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CROSSREFS
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Sequence in context: A164420 A164457 A164419 * A134035 A351620 A078157
Adjacent sequences: A164477 A164478 A164479 * A164481 A164482 A164483
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KEYWORD
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nonn,easy
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AUTHOR
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R. H. Hardin, Aug 14 2009
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EXTENSIONS
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Edited by Alois P. Heinz, Oct 27 2017
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STATUS
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approved
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