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A253121
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Numbers n such that the hexagonal number H(n) is equal to the sum of the octagonal numbers O(m), O(m+1), O(m+2) and O(m+3) for some m.
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2
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18, 1730, 169498, 16609050, 1627517378, 159480093970, 15627421691658, 1531327845688490, 150054501455780338, 14703809814820784610, 1440823307350981111418, 141185980310581328134330, 13834785247129619176052898, 1355667768238392097925049650
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OFFSET
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1,1
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COMMENTS
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Also positive integers y in the solutions to 24*x^2-4*y^2+56*x+2*y+60 = 0, the corresponding values of x being A253120.
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LINKS
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FORMULA
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a(n) = 99*a(n-1)-99*a(n-2)+a(n-3).
G.f.: -2*x*(5*x^2-26*x+9) / ((x-1)*(x^2-98*x+1)).
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EXAMPLE
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18 is in the sequence because H(18) = 630 = 96+133+176+225 = O(6)+O(7)+O(8)+O(9).
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PROG
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(PARI) Vec(-2*x*(5*x^2-26*x+9)/((x-1)*(x^2-98*x+1)) + O(x^100))
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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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