A197353 a(0)=0, a(1)=1, a(2n)=19*a(n), a(2n+1)=a(2n)+1.
0, 1, 19, 20, 361, 362, 380, 381, 6859, 6860, 6878, 6879, 7220, 7221, 7239, 7240, 130321, 130322, 130340, 130341, 130682, 130683, 130701, 130702, 137180, 137181, 137199, 137200, 137541, 137542, 137560, 137561, 2476099, 2476100, 2476118, 2476119
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Hsien-Kuei Hwang, Svante Janson, and Tsung-Hsi Tsai, Identities and periodic oscillations of divide-and-conquer recurrences splitting at half, arXiv:2210.10968 [cs.DS], 2022, p. 45.
Programs
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Magma
[n: n in [0..2500000] | Set(IntegerToSequence(n, 19)) subset {0, 1}]; // Vincenzo Librandi, Jun 05 2012 -
Mathematica
FromDigits[#,19]&/@Tuples[{0,1},5] (* Vincenzo Librandi, Jun 05 2012 *)
Formula
a(n) = Sum_{k>=0} A030308(n,k)*19^k.
G.f.: (1/(1 - x))*Sum_{k>=0} 19^k*x^(2^k)/(1 + x^(2^k)). - Ilya Gutkovskiy, Jun 04 2017
Comments