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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
OFFSET
1,1
COMMENTS
Positive integers y in the solutions to 2*x^2-27*y^2-729*y-6552 = 0.
LINKS
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 *)
Position[Total/@Partition[Accumulate[Range[70000]], 27, 1], _?(IntegerQ[ Sqrt[ #]]&)]//Flatten (* The program generates the first 22 terms of the sequence. To generate more, increase the Range constant but the program may take a long time to run. *) (* Harvey P. Dale, Jul 27 2021 *)
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. A116476 (length 11), A257293 (length 13), A257707 (length 23), A257708 (length 25), A257710 (length 37).
Sequence in context: A236332 A220037 A144840 * A121866 A301961 A250478
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 04 2015
STATUS
approved