

A279041


Expansion of Product_{k>=1} 1/(1  x^(k*(3*k2))).


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
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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, 226228 (1995), 5772; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]


FORMULA

G.f.: Product_{k>=1} 1/(1  x^(k*(3*k2))).


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*t2)>n, t1, t))(1+h(n1)))
end:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
b(n, i1)+(t> b(nt, min(i, h(nt))))(i*(3*i2))))
end:
a:= n> b(n, h(n)):


MATHEMATICA

nmax=90; CoefficientList[Series[Product[1/(1  x^(k (3 k  2))), {k, 1, nmax}], {x, 0, nmax}], x]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



