|
%I #27 Jan 26 2018 13:10:45
%S 11,36,140,540,2108,8316,33020,131580,525308,2099196,8392700,33562620,
%T 134234108,536903676,2147549180,8590065660,34360000508,137439477756,
%U 549756862460,2199025352700,8796097216508,35184380477436,140737505132540,562949986975740,2251799880794108,9007199388958716,36028797287399420
%N Least k such that k-1 and k+1 in binary representation have same number n of 0's as 1's.
%H Colin Barker, <a href="/A191296/b191296.txt">Table of n, a(n) for n = 2..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F a(n) = 2*(2^(n-1) + 2)*(2^(n-1) - 1) for n>=3. - _Nathaniel Johnston_, May 30 2011
%F a(0)=11, a(1)=36, a(2)=140, a(3)=540, a(n)=7*a(n-1)-14*a(n-2)+8*a(n-3). - _Harvey P. Dale_, Jun 10 2011
%F G.f.: x^2*(11 - 41*x + 42*x^2 - 24*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)). - _Colin Barker_, Jan 26 2018
%t Join[{11},LinearRecurrence[{7,-14,8},{36,140,540},40]] (* _Harvey P. Dale_, Jun 10 2011 *)
%o (PARI) a(n)=if(n<3,11,2*(2^(n-1) + 2)*(2^(n-1) - 1)) \\ _Charles R Greathouse IV_, Jun 01 2011
%o (PARI) Vec(x^2*(11 - 41*x + 42*x^2 - 24*x^3) / ((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^40)) \\ _Colin Barker_, Jan 26 2018
%Y Cf. A031443 (digitally balanced numbers), A191292, A191341.
%K nonn,easy,base
%O 2,1
%A _Juri-Stepan Gerasimov_, May 29 2011
%E a(11)-a(27) and recurrence from _Charles R Greathouse IV_, May 29 2011
|
