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A144929
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Numbers n such that there exists an integer k with (n+1)^3-n^3=7*k^2.
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3
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1, 166, 18313, 2014318, 221556721, 24369225046, 2680393198393, 294818882598238, 32427396692607841, 3566718817304264326, 392306642506776468073, 43150163956928107223758, 4746125728619585018145361, 522030679984197423888766006, 57418628672533097042746115353, 6315527123298656477278183922878
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (111,-111,1)
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FORMULA
| a(n+2)=110*a(n+1)-a(n)+54
a(n)=-(1/2)+(3/4)*{[55+12*sqrt(21)]^n+[55-12*sqrt(21)]^n}+(1/6)*sqrt(21)*{[55+12*sqrt(21)]^n-[55-12*sqrt(21)]^n }, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 25 2008]
a(n)=111*a(n-1)-111*a(n-2)+a(n-3), n>3. [From Harvey P. Dale, June 11 2011]
G.f.: x*(-1-55*x+2*x^2) ) / ( (x-1)*(x^2-110*x+1) ). [From Harvey P. Dale, June 11 2011]
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EXAMPLE
| a(1)=1 because 2^3-1^3=7=7*1^2
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MATHEMATICA
| RecurrenceTable[{a[1]==1, a[2]==166, a[n]==54+110a[n-1]-a[n-2]}, a[n], {n, 20}] (* or *) LinearRecurrence[{111, -111, 1}, {1, 166, 18313}, 20] (* From Harvey P. Dale, June 11 2011 *)
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CROSSREFS
| Cf. A144927, A144928, A144930.
Sequence in context: A204963 A011815 A188413 * A163398 A097400 A142664
Adjacent sequences: A144926 A144927 A144928 * A144930 A144931 A144932
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KEYWORD
| nonn
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AUTHOR
| Richard Choulet (richardchoulet(AT)yahoo.fr), Sep 25 2008
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