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A252116
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Numbers n such that the pentagonal number P(n) is equal to the sum of the heptagonal numbers H(m), H(m+1) and H(m+2) for some m.
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2
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1283, 60266, 133006667, 6248482130, 13790397229331, 647855124125114, 1429815965398472795, 67170914973291570338, 148246178910654059084579, 6964414805612961471642122, 15370460320384618188608829803, 722084455808392156329506905586
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OFFSET
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1,1
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COMMENTS
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Also nonnegative integers y in the solutions to 15*x^2-3*y^2+21*x+y+16 = 0, the corresponding values of x being A252115.
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LINKS
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FORMULA
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G.f.: -x*(2*x^4+57*x^3-77605*x^2+58983*x+1283) / ((x-1)*(x^2-322*x+1)*(x^2+322*x+1)).
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EXAMPLE
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1283 is in the sequence because P(1283) = 2468492 = 819963+822829+825700 = H(573)+H(574)+H(575).
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MATHEMATICA
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LinearRecurrence[{1, 103682, -103682, -1, 1}, {1283, 60266, 133006667, 6248482130, 13790397229331}, 20] (* Harvey P. Dale, May 08 2020 *)
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PROG
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(PARI) Vec(-x*(2*x^4+57*x^3-77605*x^2+58983*x+1283)/((x-1)*(x^2-322*x+1)*(x^2+322*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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