A164452 Number of binary strings of length n with no substrings equal to 0001 0010 or 1101.

13, 21, 32, 48, 70, 101, 144, 204, 287, 402, 561, 781, 1085, 1505, 2085, 2886, 3992, 5519, 7627, 10537, 14554, 20099, 27753, 38318, 52901, 73030, 100814, 139164, 192098, 265162, 366011, 505211, 697346, 962546, 1328596, 1833847, 2531234

Offset

4,1

Links

R. H. Hardin, Table of n, a(n) for n = 4..500

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-2,1).

Formula

G.f.: -x^4*(13-18*x+8*x^2+2*x^3-12*x^4+8*x^5) / ( (x^4+x-1)*(x-1)^2 ). - R. J. Mathar, Jan 19 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-4) - 2*a(n-5) + a(n-6). - Wesley Ivan Hurt, Nov 17 2022

Mathematica

CoefficientList[Series[(13 - 18*x + 8*x^2 + 2*x^3 - 12*x^4 + 8*x^5)/((1 - x - x^4)*(x - 1)^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Nov 17 2022 *)

Crossrefs

Sequence in context: A282844 A020440 A164458 * A164444 A164438 A164490

Adjacent sequences: A164449 A164450 A164451 * A164453 A164454 A164455

Keyword

nonn,easy

Author

R. H. Hardin, Aug 14 2009

Status

approved