|
%I #22 May 21 2021 19:41:07
%S 0,1,3,9,33,129,513,2049,8193,32769,131073,524289,2097153,8388609,
%T 33554433,134217729,536870913,2147483649,8589934593,34359738369,
%U 137438953473,549755813889,2199023255553,8796093022209,35184372088833
%N Partial sums of A084509. Positions of ones in the first differences of A084506.
%H Guo-Niu Han, <a href="/A196265/a196265.pdf">Enumeration of Standard Puzzles</a>, 2011. [Cached copy]
%H Guo-Niu Han, <a href="https://arxiv.org/abs/2006.14070">Enumeration of Standard Puzzles</a>, arXiv:2006.14070 [math.CO], 2020.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).
%F a(n) = n for n < 2, a(n) = 2^(2*n - 3) + 1 = A087289(n-2) for n >= 2. - _Antti Karttunen_, Oct 24 2012 [Corrected by _Petros Hadjicostas_, Aug 02 2020]
%F From _Chai Wah Wu_, Jan 28 2021: (Start)
%F a(n) = 5*a(n-1) - 4*a(n-2) for n > 3.
%F G.f.: x*(-2*x^2 - 2*x + 1)/((x - 1)*(4*x - 1)). (End)
%t LinearRecurrence[{5,-4},{0,1,3,9},30] (* _Harvey P. Dale_, May 21 2021 *)
%Y Cf. A084506, A084509, A087289.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 02 2003
|
