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A200998
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Triangular numbers, T(m), that are three-quarters of another triangular number: T(m) such that 4*T(m)=3*T(k) for some k.
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2
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0, 21, 4095, 794430, 154115346, 29897582715, 5799976931385, 1125165627105996, 218276331681631860, 42344483180609474865, 8214611460706556491971, 1593592278893891349967530, 309148687493954215337208870, 59973251781548223884068553271
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OFFSET
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0,2
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COMMENTS
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For n>1, a(n) = 194*a(n-1) - a (n-2) + 21. See A200993 for generalization.
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LINKS
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FORMULA
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G.f.: (21*x)/(1 - 195*x + 195*x^2 - x^3).
a(n) = 195*a(n-1)-195*a(n-2)+a(n-3) for n>2.
a(n) = ((97+56*sqrt(3))^(-n)*(-1+(97+56*sqrt(3))^n)*(-7+4*sqrt(3)+(7+4*sqrt(3))*(97+56*sqrt(3))^n))/128.
(End)
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EXAMPLE
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4*0 = 3*0.
4*21 = 3*28.
4*4095 = 3*5640.
4*794430 = 3*1059240.
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MATHEMATICA
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LinearRecurrence[{195, -195, 1}, {0, 21, 4095}, 30] (* Vincenzo Librandi, Mar 03 2016 *)
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PROG
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(Magma) I:=[0, 21]; [n le 2 select I[n] else 194*Self(n-1) - Self(n-2) + 21: n in [1..20]]; // Vincenzo Librandi, Mar 03 2016
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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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