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 A179865 Number of n-bit binary numbers containing one run of 0's. 3
 1, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Gennady Eremin, Table of n, a(n) for n = 1..500 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA For n>=2, a(n) = A000217(n-1). G.f.: x*(1 + x/(1-x)^3). - Gennady Eremin, Feb 23 2021 For n > 1, a(n+1) = a(n) + n. - Gennady Eremin, Mar 12 2021 EXAMPLE G.f. = x + x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 15*x^6 + 21*x^7 + 28*x^8 + ... For n = 4, the 6 numbers are 1000, 1001, 1011, 1100, 1101, 1110. PROG (Python) def A179865(n):     if n==1: return 1     return n*(n-1)//2  # Gennady Eremin, Mar 14 2021 CROSSREFS Cf. A000217. Sequence in context: A253145 A161680 A000217 * A105340 A176659 A109811 Adjacent sequences:  A179862 A179863 A179864 * A179866 A179867 A179868 KEYWORD nonn,base,easy AUTHOR Vladimir Shevelev, Jul 30 2010, Aug 03 2010 EXTENSIONS Edited by N. J. A. Sloane, Aug 08 2010 More terms from Michel Marcus, Feb 23 2021 STATUS approved

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Last modified May 13 06:11 EDT 2021. Contains 343836 sequences. (Running on oeis4.)