A143662 a(n) is the number of n-tosses having a run of 6 or more heads for a fair coin (i.e., probability is a(n)/2^n).

0, 0, 0, 0, 0, 0, 1, 3, 8, 20, 48, 112, 256, 575, 1275, 2798, 6088, 13152, 28240, 60320, 128257, 271623, 573216, 1205880, 2529680, 5293264, 11050496, 23021311, 47868151, 99357390, 205897508, 426042552, 880346272, 1816750912, 3744698241, 7709963787, 15857441096, 32582726508, 66886894112

Offset: 0

Author

DoZerg (daidodo(AT)gmail.com), Aug 28 2008

Keywords

• nonn

Comments

a(n-1) is the number of compositions of n with at least one part >=7. - Joerg Arndt, Aug 06 2012

Links

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

Programs

Mathematica

LinearRecurrence[{3,-1,-1,-1,-1,-1,-2},{0,0,0,0,0,0,1},40] (* Harvey P. Dale, Dec 06 2018 *)

PARI

N=66;  x='x+O('x^N);
gf = (1-x)/(1-2*x); /* A011782(n): compositions of n */
gf -= 1/(1 - (x+x^2+x^3+x^4+x^5+x^6)); /* A001592(n+5): compositions of n into parts <=6 */
v143662=Vec(gf + 'a0);  v143662[1]=0; /* kludge to get all terms */
v143662 /* show terms */
/* Joerg Arndt, Aug 06 2012 */

Formula

G.f.: x^6/ ( (2*x-1)*(x^6+x^5+x^4+x^3+x^2+x-1) ). - Joerg Arndt, Aug 06 2012

a(n) = 2^n - A001592(n+6). - R. J. Mathar, Aug 06 2012