

A307148


Number of binary partitions of n in which exactly one of the powers of 2 is used an odd number of times.


2



0, 1, 1, 1, 2, 2, 3, 2, 5, 4, 7, 4, 10, 6, 12, 6, 17, 10, 21, 10, 28, 14, 32, 14, 42, 20, 48, 20, 60, 26, 66, 26, 83, 36, 93, 36, 114, 46, 124, 46, 152, 60, 166, 60, 198, 74, 212, 74, 254, 94, 274, 94, 322, 114, 342, 114, 402, 140, 428, 140, 494, 166, 520
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


COMMENTS

If someone extends this, the analogs L(m, n) = numbers of binary partitions of n in which exactly m of the powers of 2 are used an odd number of times for m>2 could also be added (A307149 is the case m=2).


LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
George E. Andrews and Jim Lawrence, Binary partitions and binary partition polytopes, preprint.
George E. Andrews and Jim Lawrence, Binary partitions and binary partition polytopes, Aequationes mathematicae 91.5 (2017): 859869.


MATHEMATICA

Clear[L]; L[m_, n_] := L[m, n] = If[n == 0, If[m == 0, 1, 0], If[EvenQ[n] && n >= 2, L[m, n  2] + L[m, n/2], If[m >= 1, L[m  1, n  1], 0]]]; Table[L[1, n], {n, 0, 100}] (* Vaclav Kotesovec, Mar 29 2019 *)


CROSSREFS

Cf. A000123, A307149.
Sequence in context: A065769 A280264 A219606 * A238780 A113298 A058705
Adjacent sequences: A307145 A307146 A307147 * A307149 A307150 A307151


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mar 28 2019


EXTENSIONS

More terms from Vaclav Kotesovec, Mar 29 2019


STATUS

approved



