OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Bin Lan and James A. Sellers, Properties of a Restricted Binary Partition Function a la Andrews and Lewis, #A23 INTEGERS 15 (2015), p.2.
FORMULA
G.f.: Product_{k>=1} (1 - x^(2^(2*k-2) + 2^(2*k-1))) / ((1 - x^(2^(2*k-2))) * (1 - x^(2^(2*k-1)))).
G.f.: Product_{k>=1} (1 - x^(3*2^(2*k-2))) / (1 - x^(2^(k-1))).
For n>=1 a(2*n) = a(2*n-2) + a([n/2]).
For n>=1 a(2*n+1) = a(2*n) - a(2*n-1).
EXAMPLE
a(10) = 8 where the partitions are the following: 8+2, 8+1+1, 4+4+2, 4+2+2+2, 4+4+1+1, 4+1+1+1+1+1+1, 2+2+2+2+2, 1+1+1+1+1+1+1+1+1+1.
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1-x^(3*2^(2*k-2)))/(1-x^(2^(k-1))), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[1] = 1; a[2] = 2; a[3] = 1; Flatten[{1, 1, 2, 1, Table[If[EvenQ[n], a[n] = a[n-2] + a[Floor[n/4]], a[n] = a[n-1] - a[n-2]], {n, 4, 100}]}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 24 2017
STATUS
approved