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A164452 Number of binary strings of length n with no substrings equal to 0001 0010 or 1101. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 05:22 EST 2022. Contains 358594 sequences. (Running on oeis4.)