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A200999
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Triangular numbers, T(m), that are four-thirds of another triangular number; T(m) such that 3*T(m) = 4*T(k) for some k.
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2
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0, 28, 5460, 1059240, 205487128, 39863443620, 7733302575180, 1500220836141328, 291035108908842480, 56459310907479299820, 10952815280942075322628, 2124789705191855133290040, 412198249991938953782945160, 79964335708730965178758071028
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OFFSET
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0,2
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COMMENTS
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Numbers h such that 6*h+1 and 8*h+1 are both squares. [Bruno Berselli, Jul 07 2014]
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LINKS
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FORMULA
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For n>1, a(n) = 194*a(n-1) - a (n-2) + 28. See A200998 for generalization.
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))/96.
a(n) = 195*a(n-1)-195*a(n-2)+a(n-3) for n>2.
G.f.: 28*x / ((1-x)*(1-194*x+x^2)).
(End)
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EXAMPLE
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3*0 = 4*0.
3*28 = 4*21.
3*5640 = 4*4095.
3*1059240 = 4*794430.
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MATHEMATICA
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LinearRecurrence[{195, -195, 1}, {0, 28, 5460}, 20] (* T. D. Noe, Feb 15 2012 *)
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PROG
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(PARI) concat(0, Vec(28*x/((1-x)*(1-194*x+x^2)) + O(x^15))) \\ Colin Barker, Mar 02 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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