OFFSET
0,9
LINKS
G. E. Andrews, A. S. Fraenkel, and J. A. Sellers, Characterizing the number of m-ary partitions modulo m, The American Mathematical Monthly, Vol. 122, No. 9 (November 2015), pp. 880-885.
G. E. Andrews, A. S. Fraenkel, and J. A. Sellers, Characterizing the number of m-ary partitions modulo m.
Tom Edgar, The distribution of the number of parts of m-ary partitions modulo m., arXiv:1603.00085 [math.CO], 2016.
FORMULA
Let b(0) = 1 and b(n) = b(n-1) + b(floor(n/4)) and let c(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i is the base 4 representation of n. Then a(n) = (1/4)*(b(n) - c(n)).
PROG
(Sage)
def b(n):
A=[1]
for i in [1..n]:
A.append(A[i-1] + A[i//4])
return A[n]
print([(b(n)-prod(x+1 for x in n.digits(4)))/4 for n in [0..63]])
CROSSREFS
KEYWORD
nonn
AUTHOR
Tom Edgar, Feb 04 2016
STATUS
approved