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A226881 Number of n-length binary words w with #(w,0) >= #(w,1) >= 1, where #(w,x) gives the number of digits x in w. 3
0, 0, 2, 3, 10, 15, 41, 63, 162, 255, 637, 1023, 2509, 4095, 9907, 16383, 39202, 65535, 155381, 262143, 616665, 1048575, 2449867, 4194303, 9740685, 16777215, 38754731, 67108863, 154276027, 268435455, 614429671, 1073741823, 2448023842, 4294967295, 9756737701 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: (3*x-1)/(2*(x-1)*(2*x-1)) + 1/(2*sqrt((1+2*x)*(1-2*x))).

a(n) = Sum_{i=1..floor(n/2)} C(n,i). - Wesley Ivan Hurt, Mar 14 2015

EXAMPLE

a(4) = 10: 0001, 0010, 0011, 0100, 0101, 0110, 1000, 1001, 1010, 1100.

MAPLE

a:= proc(n) option remember;

      `if`(n<4, n*(n-1)*(4-n)/2, (9*(n-1)*(n-4) *a(n-1)

      +(12-32*n+6*n^2) *a(n-2) -36*(n-2)*(n-4) *a(n-3)

      +8*(n-3)*(3*n-10) *a(n-4))/ (n*(3*n-13)))

    end:

seq(a(n), n=0..40);

MATHEMATICA

Table[Sum[Binomial[n, i], {i, Floor[n/2]}], {n, 0, 30}] (* Wesley Ivan Hurt, Mar 14 2015 *)

CROSSREFS

Column k=2 of A226874.

Sequence in context: A135101 A108065 A187767 * A026336 A027913 A081204

Adjacent sequences:  A226878 A226879 A226880 * A226882 A226883 A226884

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jun 21 2013

STATUS

approved

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Last modified October 21 20:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)