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 A257709 Numbers n such that T(n) + T(n+1) + ... + T(n+26) is a square, where T = A000217 (triangular numbers). 4
 8, 14, 39, 53, 103, 112, 206, 264, 509, 647, 1141, 1230, 2160, 2734, 5159, 6525, 11415, 12296, 21502, 27184, 51189, 64711, 113117, 121838, 212968, 269214, 506839, 640693, 1119863, 1206192, 2108286, 2665064, 5017309, 6342327, 11085621, 11940190, 20870000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Positive integers y in the solutions to 2*x^2-27*y^2-729*y-6552 = 0. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,10,-10,0,0,0,0,-1,1). FORMULA G.f.: x*(2*x^12+x^11+6*x^10+2*x^9+5*x^8+2*x^7-14*x^6-9*x^5-50*x^4-14*x^3-25*x^2-6*x-8) / ((x-1)*(x^12-10*x^6+1)). MATHEMATICA LinearRecurrence[{1, 0, 0, 0, 0, 10, -10, 0, 0, 0, 0, -1, 1}, {8, 14, 39, 53, 103, 112, 206, 264, 509, 647, 1141, 1230, 2160}, 50] (* Vincenzo Librandi, May 05 2015 *) PROG (PARI) Vec(x*(2*x^12+x^11+6*x^10+2*x^9+5*x^8+2*x^7-14*x^6-9*x^5-50*x^4-14*x^3-25*x^2-6*x-8) / ((x-1)*(x^12-10*x^6+1)) + O(x^100)) (MAGMA) I:=[8, 14, 39, 53, 103, 112, 206, 264, 509, 647, 1141, 1230, 2160]; [n le 13 select I[n] else Self(n-1)+10*Self(n-6)-10*Self(n-7)-Self(n-12)+Self(n-13): n in [1..40]]; // Vincenzo Librandi, May 05 2015 CROSSREFS Cf. A176541, A176542, A000217, A000292, A001110, A077415. Cf. A116476 (length 11), A257293 (length 13), A257707 (length 23), A257708 (length 25), A257710 (length 37). Sequence in context: A236332 A220037 A144840 * A121866 A301961 A250478 Adjacent sequences:  A257706 A257707 A257708 * A257710 A257711 A257712 KEYWORD nonn,easy AUTHOR Colin Barker, May 04 2015 STATUS approved

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Last modified February 20 07:41 EST 2020. Contains 332069 sequences. (Running on oeis4.)