A307148 Number of binary partitions of n in which exactly one of the powers of 2 is used an odd number of times.

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

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): 859-869.

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 A330545 A113298

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