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A333818
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G.f.: Sum_{k>=1} x^(k*(3*k - 2)) / (1 - x^(6*k)).
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6
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1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1
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OFFSET
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1
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COMMENTS
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Number of ways to write n as the difference of two octagonal numbers.
a(n) = 2 if n = 133, 175, 176, 217, 224, 259, 272, 280, 301, 320, 343, 368, 385, 400, ... a(n) = 3 if n = 560, 637, 896, 935, ... a(n) = 4 if n = 1729, 2240, 2275, ... - R. J. Mathar, Oct 08 2020 [modified by Ilya Gutkovskiy, Oct 09 2020]
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LINKS
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FORMULA
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G.f.: Sum_{i>=0} Sum_{j>=i} Product_{k=i..j} x^(6*k + 1).
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EXAMPLE
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a(1729) = 4 with representations 1729 = 1825-96 = 2465-736 = 5985-4256 = 249985-248256. - R. J. Mathar, Oct 08 2020
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MAPLE
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local a, hi, hiO, lo, loO;
a := 0 ;
for hi from 1 do
for lo from hi-1 to 1 by -1 do
if lo = hi-1 and hiO-loO > n then
return a;
end if;
if hiO-loO = n then
a := a+1 ;
elif hiO-loO > n then
break;
end if ;
end do:
end do:
end proc:
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MATHEMATICA
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nmax = 95; CoefficientList[Series[Sum[x^(k (3 k - 2))/(1 - x^(6 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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