login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A268443 a(n) = (A005705(n) - A268444(n))/4. 1
0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 6, 6, 6, 6, 11, 12, 13, 14, 17, 18, 19, 20, 25, 26, 27, 28, 35, 36, 37, 38, 49, 52, 55, 58, 64, 67, 70, 73, 82, 85, 88, 91, 103, 106, 109, 112, 130, 136, 142, 148, 158, 164, 170, 176, 190, 196, 202, 208, 226, 232, 238, 244 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..63.

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[floor(i/4)])

    return A[n]

print [(b(n)-prod(x+1 for x in n.digits(4)))/4 for n in [0..63]]

CROSSREFS

Cf. A005705, A268444, A268127, A268128.

Sequence in context: A196186 A075753 A006166 * A142716 A211515 A260740

Adjacent sequences:  A268440 A268441 A268442 * A268444 A268445 A268446

KEYWORD

nonn

AUTHOR

Tom Edgar, Feb 04 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 27 19:10 EST 2020. Contains 332308 sequences. (Running on oeis4.)