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A268127 a(n) = (A005704(n)-A006047(n))/3. 3
0, 0, 0, 1, 1, 1, 3, 3, 3, 7, 8, 9, 12, 13, 14, 19, 20, 21, 30, 33, 36, 42, 45, 48, 57, 60, 63, 79, 86, 93, 103, 111, 119, 132, 141, 150, 168, 180, 192, 209, 222, 235, 257, 271, 285, 316, 335, 354, 380, 400, 420, 453, 474, 495, 543, 573, 603, 639, 672, 705, 747 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
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/3)) and let c(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*3^i is the ternary representation of n. Then a(n) = (1/3)*(b(n) - c(n)).
MATHEMATICA
b[n_] := b[n] = If[n <= 2, n+1, b[n-1] + b[Floor[n/3]]];
c = Nest[Join[#, 2#, 3#]&, {1}, 4];
a[n_] := (b[n] - c[[n+1]])/3;
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Dec 12 2018 *)
PROG
(Sage)
def b(n):
A=[1]
for i in [1..n]:
A.append(A[i-1] + A[floor(i/3)])
return A[n]
[(b(n)-prod(x+1 for x in n.digits(3)))/3 for n in [0..60]]
CROSSREFS
Sequence in context: A031503 A049500 A227826 * A200076 A342335 A137438
KEYWORD
nonn
AUTHOR
Tom Edgar, Jan 26 2016
STATUS
approved

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Last modified May 27 06:20 EDT 2024. Contains 372848 sequences. (Running on oeis4.)