

A179865


Number of nbit 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
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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(n1).
G.f.: x*(1 + x/(1x)^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*(n1)//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



