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Numbers such that every run length in base 2 is 4.
2

%I #12 Apr 13 2018 09:35:46

%S 15,240,3855,61680,986895,15790320,252645135,4042322160,64677154575,

%T 1034834473200,16557351571215,264917625139440,4238682002231055,

%U 67818912035696880,1085102592571150095,17361641481138401520

%N Numbers such that every run length in base 2 is 4.

%C a(n) is the number whose binary representation is A154805(n).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (16,1,-16).

%F Conjecture: a(n) = 1/17*2^(4*n+4) + 15/34*(-1)^(n+1) - 1/2. - _Vaclav Kotesovec_, Nov 30 2012

%F Empirical g.f.: 15*x / ((x-1)*(x+1)*(16*x-1)). - _Colin Barker_, Sep 16 2013

%t LinearRecurrence[{16,1,-16},{15,240,3855},20] (* _Harvey P. Dale_, Apr 13 2018 *)

%Y Cf. A043291, A097262, A152776, A154805, A154808.

%K easy,nonn

%O 1,1

%A _Omar E. Pol_, Jan 25 2009

%E More terms from _Sean A. Irvine_, Feb 21 2010