The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309616 a(n) is the number of ways to represent 2*n in the decibinary system. 0
 1, 2, 4, 6, 10, 13, 18, 22, 30, 36, 45, 52, 64, 72, 84, 93, 110, 122, 140, 154, 177, 192, 214, 230, 258, 277, 304, 324, 356, 376, 405, 426, 464, 490, 528, 557, 604, 634, 678, 710, 765, 802, 854, 892, 952, 989, 1042, 1080, 1146, 1190, 1253, 1300, 1374, 1420, 1486, 1533, 1612, 1664 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It appears that a(n) is the number of decibinary numbers that can be constructed to represent the decimal numbers 2n-2 and 2n-1. To make this more clear let's consider n = 5: a(5) = 10 means that there are 10 decibinary numbers that represent the decimal numbers 2*5 - 2 = 8 and 2*5 - 1 = 9. Furthermore, a(n) is the number of k such that A028897(k)=2*n. LINKS HackerRank, Decibinary Numbers FORMULA a(1) = 1. a(n) = a(n-1) + a(ceiling(n/2)) if 1 < n <= 5. a(n) = a(n-1) + a(ceiling(n/2)) - a(ceiling((n-5)/2)) if n > 5. (conjectured) I think this sequence is closely related to the 10th binary partition function. The only difference is that every second number is omitted. At the moment the 10th binary partition function is not in OEIS. However, my experiments strongly suggest that the 10th binary partition function would indeed look like 1, 1, 2, 2, 4, 4, 6, 6, 10, 10, 13, 13, ... EXAMPLE a(1) = 1. a(2) = a(2-1) + a(ceiling(2/2)) = a(1) + a(1) = 1 + 1 = 2. a(3) = a(3-1) + a(ceiling(3/2)) = a(2) + a(2) = 2 + 2 = 4. a(4) = a(4-1) + a(ceiling(4/2)) = a(3) + a(2) = 4 + 2 = 6. a(5) = a(5-1) + a(ceiling(5/2)) = a(4) + a(3) = 6 + 4 = 10. a(6) = a(6-1) + a(ceiling(6/2)) - a(ceiling((6-5)/2)) = a(5) + a(3) - a(1) = 10 + 4 - 1 = 13. a(7) = a(7-1) + a(ceiling(7/2)) - a(ceiling((7-5)/2)) = a(6) + a(4) - a(1) = 13 + 6 - 1 = 18. a(8) = a(8-1) + a(ceiling(8/2)) - a(ceiling((8-5)/2)) = a(7) + a(4) - a(2) = 18 + 6 - 2 = 22. a(9) = a(9-1) + a(ceiling(9/2)) - a(ceiling((9-5)/2)) = a(8) + a(5) - a(2) = 22 + 10 - 2 = 30. a(10) = a(10-1) + a(ceiling(10/2)) - a(ceiling((10-5)/2)) = a(9) + a(5) - a(3) = 30 + 10 - 4 = 36. MATHEMATICA Nest[Append[#1, #1[[-1]] + #1[[Ceiling[#2/2] ]] - If[#2 > 5, #1[[Ceiling[(#2 - 5)/2] ]], 0 ]] & @@ {#, Length@ # + 1} &, {1}, 57] (* Michael De Vlieger, Sep 29 2019 *) PROG (C++) int a(int n) {     std::vector seq;     int a = 1;     seq.push_back(a);     for (int i = 1; i < n; i++) {         a += seq.at(i / 2);         a -= (i >= 5) ? seq.at((i - 5) / 2) : 0;         seq.push_back(a);     }     return seq.back(); } CROSSREFS Cf. A007728: superseeker found that the deltas of the sequence a(n+1) - a(n) match transformations of the original query. Cf. A028897. Sequence in context: A334821 A275489 A153817 * A267452 A140652 A007981 Adjacent sequences:  A309613 A309614 A309615 * A309617 A309618 A309619 KEYWORD nonn,base AUTHOR Jonas Hollm, Aug 10 2019 EXTENSIONS Name corrected by Rémy Sigrist, Oct 15 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 25 23:09 EDT 2021. Contains 347664 sequences. (Running on oeis4.)