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A279042
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Numbers k such that 2*k+1 and 10*k+1 are both triangular numbers (A000217).
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1
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4455, 30537, 461938302, 3166172226, 47894687058501, 328275068740587, 4965816943137597372, 34036215673995404100, 514865832250497683700195, 3528942913182916419190605, 53382319214430283898266055610, 365887859090594924500524938502
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OFFSET
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1,1
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..350
Index entries for linear recurrences with constant coefficients, signature (1,103682,-103682,-1,1).
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FORMULA
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a(n) = a(n-1) + 103682*a(n-2) - 103682*a(n-3) - a(n-4) + a(n-5) for n>5.
G.f.: 81*x*(55 + 322*x + 55*x^2) / ((1 - x)*(1 - 322*x + x^2)*(1 + 322*x + x^2)).
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EXAMPLE
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4455 is in the sequence because 2*4455+1 = 8911 and 10*4455+1 = 44551 are both triangular numbers.
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MATHEMATICA
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LinearRecurrence[{1, 103682, -103682, -1, 1}, {4455, 30537, 461938302, 3166172226, 47894687058501}, 20] (* Vincenzo Librandi, Dec 05 2016 *)
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PROG
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(PARI) Vec(81*x*(55 + 322*x + 55*x^2) / ((1 - x)*(1 - 322*x + x^2)*(1 + 322*x + x^2)) + O(x^15))
(PARI) isok(k) = ispolygonal(2*k+1, 3) & ispolygonal(10*k+1, 3)
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CROSSREFS
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Cf. A000217, A124174, A274579, A274603, A274680, A274756, A274832.
Sequence in context: A280485 A236906 A184611 * A253697 A253704 A235015
Adjacent sequences: A279039 A279040 A279041 * A279043 A279044 A279045
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Dec 04 2016
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STATUS
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approved
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