A116476 Numbers n such that T(n) + T(n+1) + ... + T(n+10) is a square, where T(m) = A000217(m) is the m-th triangular number.

13, 46, 229, 1608, 7335, 20304, 92391, 635710, 2892133, 8001886, 36403981, 250470288, 1139495223, 3152724936, 14343078279, 98684659918, 448958227885, 1242165625054, 5651136440101, 38881505539560, 176888402293623, 489410103548496

Offset: 1

Author

Edward Fedorovich (chipramy(AT)012.net.il), Mar 29 2006

Keywords

• nonn
• easy

Comments

Positive integers n such that 11*n^2 + 121*n + 440 = 2*m^2 for some integer m. - Max Alekseyev, Jan 20 2010

Examples

			13 belongs to this sequence since T(13) + T(14) + ... + T(23) = 91 + 105 + 120 + 136 + 153 + 171 + 190 + 210 + 231 + 253 + 276 = 1936 = 44^2.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,394,-394,0,0,-1,1).

Crossrefs

Cf. A176541, A176542, A165517, A202391

Programs

Mathematica

For[n = 1, n < 100000, n++, If[IntegerQ[Sqrt[Sum[i*(i+1)/2, {i, n, n + 10}]]], Print[n]]] (* Stefan Steinerberger, Mar 30 2006 *)
LinearRecurrence[{1,0,0,394,-394,0,0,-1,1},{13,46,229,1608,7335,20304,92391,635710,2892133},30] (* Harvey P. Dale, Sep 01 2017 *)

Formula

For n>8, a(n) = 394*a(n-4) - a(n-8) + 2156. - Max Alekseyev, Jan 20 2010

G.f.: x*(2*x^8+7*x^7+15*x^6+33*x^5-605*x^4-1379*x^3-183*x^2-33*x-13)/((x-1)*(x^8-394*x^4+1)). - Colin Barker, Nov 22 2012

Extensions

Extended by Max Alekseyev, Jan 20 2010