

A116476


Numbers n such that T(n) + T(n+1) + ... + T(n+10) is a square, where T(m) = A000217(m) is the mth 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
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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(n4)  a(n8) + 2156.  Max Alekseyev, Jan 20 2010
G.f.: x*(2*x^8+7*x^7+15*x^6+33*x^5605*x^41379*x^3183*x^233*x13)/((x1)*(x^8394*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



