A158745 a(3n)=A130750(n). a(3n+1)=A130752(n). a(3n+2)=A130755(n).

1, 2, 3, 3, 5, 4, 8, 9, 7, 17, 16, 15, 33, 31, 32, 64, 63, 65, 127, 128, 129, 255, 257, 256, 512, 513, 511, 1025, 1024, 1023, 2049, 2047, 2048, 4096, 4095, 4097, 8191, 8192, 8193, 16383, 16385, 16384, 32768, 32769, 32767, 65537, 65536, 65535, 131073, 131071, 131072, 262144

Offset: 0

Author

Paul Curtz, Mar 25 2009

Keywords

• nonn
• less

Comments

This mixes three sequences which are identical to their third differences.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 0, 3, 0, 0, -3, 0, 0, 2).

Crossrefs

Cf. A138635, A140430, A130785, A140495.

Programs

Mathematica

LinearRecurrence[{0,0,3,0,0,-3,0,0,2},{1,2,3,3,5,4,8,9,7},60] (* Harvey P. Dale, Mar 12 2023 *)

Formula

a(3n)+a(3n+1)+a(3n+2)= A007283(n+1).

a(18n) = A130750(6n)= 2^(6n+1)-1.

a(n) = 3*a(n-3)-3*a(n-6)+2*a(n-9). G.f.: -(1+2*x+3*x^2-x^4-5*x^5+2*x^6+4*x^8)/((2*x^3-1)*(x^6-x^3+1)). - R. J. Mathar, Jan 23 2009

Extensions

Edited and extended by R. J. Mathar, Apr 09 2009