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 A164413 Number of binary strings of length n with no substrings equal to 0000, 0001 or 1001. 1
 1, 2, 4, 8, 13, 22, 36, 58, 94, 152, 246, 398, 644, 1042, 1686, 2728, 4414, 7142, 11556, 18698, 30254, 48952, 79206, 128158, 207364, 335522, 542886, 878408, 1421294, 2299702, 3720996, 6020698, 9741694, 15762392, 25504086, 41266478, 66770564, 108037042 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Essentially the same as A022112. - R. J. Mathar, Nov 30 2011 LINKS David A. Corneth, Table of n, a(n) for n = 0..1999 (terms n = 4..500 from R. H. Hardin) Index entries for linear recurrences with constant coefficients, signature (1,1). FORMULA From Colin Barker, Oct 27 2017: (Start) G.f.: -(x^2+1)*(x^2-x+1)*(x+1)^2/(x^2+x-1). a(n) = 2*(((1 - sqrt(5))/2)^n + ((1 + sqrt(5))/2)^n) for n>4. a(n) = a(n-1) + a(n-2) for n>6. (End) PROG (PARI) Vec(-(x^2+1)*(x^2-x+1)*(x+1)^2/(x^2+x-1) + O(x^50)) \\ Colin Barker, Oct 27 2017 (PARI) first(n) = {my(start = [1, 2, 4, 8, 13, 22, 36]); if(n <= 7, return(vector(n+1, i, start[i]))); res = concat(start, vector(n-7)); for(i=8, n, res[i] = res[i-1] + res[i-2]); res} \\ David A. Corneth, Oct 27 2017 CROSSREFS Sequence in context: A207033 A291553 A244985 * A164441 A023600 A164428 Adjacent sequences:  A164410 A164411 A164412 * A164414 A164415 A164416 KEYWORD nonn,easy AUTHOR R. H. Hardin, Aug 14 2009 STATUS approved

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