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A252077
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Numbers n such that the hexagonal number X(n) is equal to the sum of the heptagonal number H(m) and H(m+1) for some m.
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2
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1, 769, 1108537, 1598509225, 2305049193553, 3323879338593841, 4793031701203124809, 6911548389255567380377, 9966447984274826959378465, 14371611081775911219856365793, 20723853213472879704205920094681, 29883781962216810757553716920163849
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OFFSET
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1,2
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COMMENTS
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Also nonnegative integers y in the solutions to 10*x^2-4*y^2+4*x+2*y+2 = 0, the corresponding values of x being A252076.
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..317
Index entries for linear recurrences with constant coefficients, signature (1443,-1443,1).
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FORMULA
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a(n) = 1443*a(n-1)-1443*a(n-2)+a(n-3).
G.f.: -x*(313*x^2-674*x+1) / ((x-1)*(x^2-1442*x+1)).
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EXAMPLE
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769 is in the sequence because X(769) = 1181953 = 589761+592192 = H(486)+H(487).
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PROG
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(PARI) Vec(-x*(313*x^2-674*x+1)/((x-1)*(x^2-1442*x+1)) + O(x^100))
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CROSSREFS
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Cf. A000384, A000566, A252076.
Sequence in context: A229854 A217495 A216646 * A236784 A205622 A205357
Adjacent sequences: A252074 A252075 A252076 * A252078 A252079 A252080
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Dec 13 2014
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STATUS
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approved
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