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
Keywords
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.
Programs
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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 *)
Extensions
More terms from Vaclav Kotesovec, Mar 29 2019
Comments