A307149 Number of binary partitions of n in which exactly two of the powers of 2 are used an odd number of times.

0, 0, 0, 1, 0, 2, 1, 3, 1, 5, 3, 7, 4, 10, 7, 12, 8, 17, 13, 21, 16, 28, 23, 32, 27, 42, 37, 48, 44, 60, 56, 66, 64, 83, 81, 93, 94, 114, 115, 124, 131, 152, 159, 166, 182, 198, 214, 212, 241, 254, 283, 274, 320, 322, 368, 342, 412, 402, 472, 428, 528, 494

Offset: 0

Author

N. J. A. Sloane, Mar 28 2019

Keywords

• nonn

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.

Crossrefs

Cf. A000123, A307148.

Programs

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[2, n], {n, 0, 100}] (* Vaclav Kotesovec, Mar 29 2019 *)

Extensions

More terms from Vaclav Kotesovec, Mar 29 2019