OFFSET
0,5
COMMENTS
Also known as the hyper 4-ary partition sequence, often denoted h_4(n).
Contains A002487 as a subsequence.
LINKS
Timothy B. Flowers, Table of n, a(n) for n = 0..10000
K. Courtright and J. Sellers, Arithmetic properties for hyper m-ary partition functions, Integers, 4 (2004), A6.
Timothy B. Flowers, Extending a Recent Result on Hyper m-ary Partition Sequences, Journal of Integer Sequences, Vol. 20 (2017), #17.6.7.
T. B. Flowers and S. R. Lockard, Identifying an m-ary partition identity through an m-ary tree, Integers, 16 (2016), A10.
FORMULA
G.f.: Product((1-x^(5*4^j))/(1-x^(4^j))), j=0..infinity).
G.f.: Product(1+x^(4^j)+x^(2*4^j)+x^(3*4^j)+x^(4*4^j), j=0..infinity).
a(0)=1 and for n>0, a(4n)=a(n)+a(n-1), a(4n+r)=a(n) for r=1,2,3.
G.f. A(x) satisfies: A(x) = (1 + x + x^2 + x^3 + x^4) * A(x^4). - Ilya Gutkovskiy, Jul 09 2019
EXAMPLE
a(72) = 4 because 72 = 64+4+4 = 64+4+1+1+1+1 = 16+16+16+16+4+4 = 16+16+16+16+4+1+1+1+1.
MATHEMATICA
n:=250;
r:=3;
(* To get up to n-th term, need r such that 4^r < n < 4^(r+1) *)
h4 := CoefficientList[ Series[ Product[ (1 - q^(5*4^i))/(1 - q^(4^i)) , {i, 0, r}], {q, 0, n} ], q]
CROSSREFS
KEYWORD
nonn
AUTHOR
Timothy B. Flowers, Nov 03 2016
STATUS
approved