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A279041 Expansion of Product_{k>=1} 1/(1 - x^(k*(3*k-2))). 5
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 10, 10, 11, 11, 11, 12, 12, 12, 14, 14, 15, 15, 15, 16, 16, 16, 18, 18, 19, 19, 19, 21, 21, 22, 24, 25, 26, 26, 26, 28, 28, 29, 31, 32, 33, 33, 33, 35, 35, 36, 39, 40, 42, 42, 43, 45, 46, 47, 50, 51, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
COMMENTS
Number of partitions of n into nonzero octagonal numbers (A000567).
LINKS
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Eric Weisstein's World of Mathematics, Octagonal Number
FORMULA
G.f.: Product_{k>=1} 1/(1 - x^(k*(3*k-2))).
EXAMPLE
a(9) = 2 because we have [8, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1].
MAPLE
h:= proc(n) option remember; `if`(n<1, 0, (t->
`if`(t*(3*t-2)>n, t-1, t))(1+h(n-1)))
end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i-1)+(t-> b(n-t, min(i, h(n-t))))(i*(3*i-2))))
end:
a:= n-> b(n, h(n)):
seq(a(n), n=0..100); # Alois P. Heinz, Dec 28 2018
MATHEMATICA
nmax=90; CoefficientList[Series[Product[1/(1 - x^(k (3 k - 2))), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A214956 A209899 A111898 * A072746 A179528 A105390
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 04 2016
STATUS
approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)