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A154150
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Numbers k such that 24 plus the k-th triangular number is a perfect square.
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3
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1, 15, 24, 94, 145, 551, 848, 3214, 4945, 18735, 28824, 109198, 168001, 636455, 979184, 3709534, 5707105, 21620751, 33263448, 126014974
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OFFSET
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1,2
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LINKS
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FORMULA
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Conjectures: (Start)
a(n) = +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).
G.f.: x*(-1-14*x-3*x^2+14*x^3+2*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)).
G.f.: ( 4 + 1/(x-1) + (10+27*x)/(x^2-2*x-1) + (-7+4*x)/(x^2+2*x-1) )/2. (End)
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EXAMPLE
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1, 5, 24, and 94 are terms:
1* (1+1)/2 + 24 = 5^2,
15*(15+1)/2 + 24 = 12^2,
24*(24+1)/2 + 24 = 18^2,
94*(94+1)/2 + 24 = 67^2.
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MATHEMATICA
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Select[Range[12602*10^4], IntegerQ[Sqrt[24+(#(#+1))/2]]&] (* Harvey P. Dale, Jul 07 2019 *)
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PROG
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(PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 24), print1(n, ", ") ) ); }
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CROSSREFS
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KEYWORD
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nonn,less
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AUTHOR
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STATUS
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approved
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