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

1, 5, 13, 25, 41, 65, 89, 125, 157, 205, 253, 325, 373, 445, 517, 625, 689, 785, 881, 1025, 1121, 1265, 1409, 1625, 1721, 1865, 2009, 2225, 2369, 2585, 2801, 3125, 3253, 3445, 3637, 3925, 4117, 4405, 4693, 5125, 5317, 5605, 5893, 6325, 6613, 7045, 7477, 8125, 8317, 8605, 8893, 9325, 9613, 10045

Offset: 1

Author

N. J. A. Sloane, Feb 16 2016

Keywords

• nonn

Links

• K.-N. Chang and S.-C. Tsai, Exact solution of a minimal recurrence, Inform. Process. Lett. 75 (2000), 61-64.

Crossrefs

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.

Programs

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

PARI

a(n) = if (n==1, 1, 2*a(ceil(n/2))+3*a(floor(n/2))); \\ Michel Marcus, Aug 30 2016