Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #12 Sep 08 2022 08:46:15
%S 1,5,13,25,41,65,89,125,157,205,253,325,373,445,517,625,689,785,881,
%T 1025,1121,1265,1409,1625,1721,1865,2009,2225,2369,2585,2801,3125,
%U 3253,3445,3637,3925,4117,4405,4693,5125,5317,5605,5893,6325,6613,7045,7477,8125,8317,8605,8893,9325,9613,10045
%N a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s)=(2,3).
%H K.-N. Chang and S.-C. Tsai, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00076-4">Exact solution of a minimal recurrence</a>, Inform. Process. Lett. 75 (2000), 61-64.
%o (PARI) a(n) = if (n==1, 1, 2*a(ceil(n/2))+3*a(floor(n/2))); \\ _Michel Marcus_, Aug 30 2016
%o (Magma) [n le 1 select 1 else 2*Self(Ceiling(n/2))+3*Self(Floor(n/2)): n in [1..60]]; // _Vincenzo Librandi_, Aug 30 2016
%Y Sequences of form a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s) = (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), (1,4), (2,3), (3,2), (4,1): A000027, A006046, A064194, A130665, A073121, A268524, A116520, A268525, A268526, A268527.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Feb 16 2016