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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. 11
13, 46, 229, 1608, 7335, 20304, 92391, 635710, 2892133, 8001886, 36403981, 250470288, 1139495223, 3152724936, 14343078279, 98684659918, 448958227885, 1242165625054, 5651136440101, 38881505539560, 176888402293623, 489410103548496 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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).

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A176541, A176542, A165517, A202391

Sequence in context: A219905 A326163 A034462 * A299716 A035340 A127305

Adjacent sequences:  A116473 A116474 A116475 * A116477 A116478 A116479

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

Extended by Max Alekseyev, Jan 20 2010

STATUS

approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)