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 A279042 Numbers k such that 2*k+1 and 10*k+1 are both triangular numbers (A000217). 1
 4455, 30537, 461938302, 3166172226, 47894687058501, 328275068740587, 4965816943137597372, 34036215673995404100, 514865832250497683700195, 3528942913182916419190605, 53382319214430283898266055610, 365887859090594924500524938502 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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). FORMULA 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)). EXAMPLE 4455 is in the sequence because 2*4455+1 = 8911 and 10*4455+1 = 44551 are both triangular numbers. MATHEMATICA LinearRecurrence[{1, 103682, -103682, -1, 1}, {4455, 30537, 461938302, 3166172226, 47894687058501}, 20] (* Vincenzo Librandi, Dec 05 2016 *) PROG (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) CROSSREFS 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 KEYWORD nonn,easy AUTHOR Colin Barker, Dec 04 2016 STATUS approved

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Last modified May 28 22:08 EDT 2022. Contains 354122 sequences. (Running on oeis4.)