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A268525 a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s)=(2,3).

%I A268525 #12 Sep 08 2022 08:46:15
%S A268525 1,5,13,25,41,65,89,125,157,205,253,325,373,445,517,625,689,785,881,
%T A268525 1025,1121,1265,1409,1625,1721,1865,2009,2225,2369,2585,2801,3125,
%U A268525 3253,3445,3637,3925,4117,4405,4693,5125,5317,5605,5893,6325,6613,7045,7477,8125,8317,8605,8893,9325,9613,10045
%N A268525 a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s)=(2,3).
%H A268525 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 A268525 (PARI) a(n) = if (n==1, 1, 2*a(ceil(n/2))+3*a(floor(n/2))); \\ _Michel Marcus_, Aug 30 2016
%o A268525 (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 A268525 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 A268525 nonn
%O A268525 1,2
%A A268525 _N. J. A. Sloane_, Feb 16 2016