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 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). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 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). 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 MATHEMATICA LinearRecurrence[{3, -1, -1, -1, -1, -1, -2}, {0, 0, 0, 0, 0, 0, 1}, 40] (* Harvey P. Dale, Dec 06 2018 *) PROG (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 */ CROSSREFS Sequence in context: A308370 A050232 A050233 * A151975 A049610 A168150 Adjacent sequences:  A143659 A143660 A143661 * A143663 A143664 A143665 KEYWORD nonn AUTHOR DoZerg (daidodo(AT)gmail.com), Aug 28 2008 STATUS approved

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)