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A253477
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Indices of centered heptagonal numbers (A069099) which are also centered triangular numbers (A005448).
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3
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1, 10, 46, 1045, 5005, 114886, 550450, 12636361, 60544441, 1389884770, 6659338006, 152874688285, 732466636165, 16814825826526, 80564670640090, 1849477966229521, 8861381303773681, 203425761459420730, 974671378744464766, 22374984282570050725
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OFFSET
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1,2
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COMMENTS
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Also positive integers y in the solutions to 3*x^2 - 7*y^2 - 3*x + 7*y = 0, the corresponding values of x being A253476.
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LINKS
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FORMULA
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a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+9*x^3-74*x^2+9*x+1) / ((x-1)*(x^4-110*x^2+1)).
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EXAMPLE
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10 is in the sequence because the 10th centered heptagonal number is 316, which is also the 15th centered triangular number.
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MATHEMATICA
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LinearRecurrence[{1, 110, -110, -1, 1}, {1, 10, 46, 1045, 5005}, 30] (* Harvey P. Dale, Aug 13 2018 *)
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PROG
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(PARI) Vec(-x*(x^4+9*x^3-74*x^2+9*x+1)/((x-1)*(x^4-110*x^2+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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