A191296 Least k such that k-1 and k+1 in binary representation have same number n of 0's as 1's.
11, 36, 140, 540, 2108, 8316, 33020, 131580, 525308, 2099196, 8392700, 33562620, 134234108, 536903676, 2147549180, 8590065660, 34360000508, 137439477756, 549756862460, 2199025352700, 8796097216508, 35184380477436, 140737505132540, 562949986975740, 2251799880794108, 9007199388958716, 36028797287399420
Offset: 2
Links
- Colin Barker, Table of n, a(n) for n = 2..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
Programs
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Mathematica
Join[{11},LinearRecurrence[{7,-14,8},{36,140,540},40]] (* Harvey P. Dale, Jun 10 2011 *) -
PARI
a(n)=if(n<3,11,2*(2^(n-1) + 2)*(2^(n-1) - 1)) \\ Charles R Greathouse IV, Jun 01 2011
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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
Formula
a(n) = 2*(2^(n-1) + 2)*(2^(n-1) - 1) for n>=3. - Nathaniel Johnston, May 30 2011
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
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
Extensions
a(11)-a(27) and recurrence from Charles R Greathouse IV, May 29 2011