A307149 - OEIS

%I #22 Dec 18 2023 08:26:06

%S 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,

%T 44,60,56,66,64,83,81,93,94,114,115,124,131,152,159,166,182,198,214,

%U 212,241,254,283,274,320,322,368,342,412,402,472,428,528,494

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

%H Vaclav Kotesovec, <a href="/A307149/b307149.txt">Table of n, a(n) for n = 0..10000</a>

%H George E. Andrews and Jim Lawrence, <a href="https://georgeandrews1.github.io/pdf/321.pdf">Binary partitions and binary partition polytopes</a>, preprint.

%H George E. Andrews and Jim Lawrence, <a href="https://doi.org/10.1007/s00010-017-0493-8">Binary partitions and binary partition polytopes</a>, Aequationes mathematicae 91.5 (2017): 859-869.

%t 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 *)

%Y Cf. A000123, A307148.

%K nonn

%O 0,6

%A _N. J. A. Sloane_, Mar 28 2019

%E More terms from _Vaclav Kotesovec_, Mar 29 2019