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A190636
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a(n)=(n^3+3*n^7)/4.
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1
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1, 98, 1647, 12304, 58625, 210006, 617743, 1572992, 3587409, 7500250, 14615711, 26874288, 47061937, 79060814, 128145375, 201327616, 307755233, 459166482, 670405519, 960002000, 1350818721, 1870771078, 2553622127, 3439857024, 4577640625, 6023862026, 7845269823
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OFFSET
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1,2
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COMMENTS
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Each term is the difference of two cubes because ((n^3+n)/2)^3-((n^3-n)/2)^3=(n^3+3*n^7)/4. More generally, ((n^s+n)/2)^3-((n^s-n)/2)^3 = (n^3+3*n^(2s+1))/4 for any s; in this case, s=3.
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LINKS
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FORMULA
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a(n) = ((n^3+n)/2)^3 - ((n^3-n)/2)^3.
G.f.: (z^7+90*z^6+891*z^5+1816*z^4+891*z^3+90*z^2+z)/(z-1)^8.
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EXAMPLE
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58625=65^3-60^3=(5^3+3*5^7)/4; 47061937=1105^3-1092^3=(13^3 + 3*13^7)/4
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MATHEMATICA
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Table[((n^3+n)/2)^3 - ((n^3-n)/2)^3, {n, 1, 20}]
Table[1/4*(n^3+3 n^7), {n, 1, 20}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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