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A164391
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Number of binary strings of length n with no substrings equal to 0000 or 0111
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1
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14, 25, 44, 77, 134, 233, 405, 703, 1220, 2117, 3673, 6372, 11054, 19176, 33265, 57705, 100101, 173645, 301221, 522526, 906422, 1572363, 2727565, 4731484, 8207665, 14237766, 24698130, 42843633, 74320480, 128923094, 223641776, 387949454
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,1
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LINKS
| R. H. Hardin, Table of n, a(n) for n = 4..500
Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,0,-1,-1).
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FORMULA
| G.f. -x^4*(-14-11*x-5*x^2+6*x^3+12*x^4+8*x^5) / ( (x-1)*(x^5+2*x^4+2*x^3+x^2-1) ). - R. J. Mathar, Nov 28 2011
a(n) = 1.6443631... * 1.7346913...^n + O(1), where 1.7346913... is the real root of x^5 - x^3 - 2x^2 - 2x - 1. [Charles R Greathouse IV, Jan 18 2012]
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CROSSREFS
| Sequence in context: A020227 A032608 A164393 * A164392 A164390 A164388
Adjacent sequences: A164388 A164389 A164390 * A164392 A164393 A164394
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KEYWORD
| nonn,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net) Aug 14 2009
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EXTENSIONS
| Conjectured g.f. verified by Charles R Greathouse IV, Jan 18 2012
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