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A116476
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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.
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3
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13, 46, 229, 1608, 7335, 20304, 92391, 635710, 2892133, 8001886, 36403981, 250470288, 1139495223, 3152724936, 14343078279, 98684659918, 448958227885, 1242165625054, 5651136440101, 38881505539560, 176888402293623
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Positive integers n such that 11*n^2 + 121*n + 440 = 2*m^2 for some integer m. [From Max Alekseyev (maxale(AT)gmail.com), Jan 20 2010]
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FORMULA
| For n>8, a(n) = 394*a(n-4) - a(n-8) + 2156. [From Max Alekseyev (maxale(AT)gmail.com), Jan 20 2010]
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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.
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MATHEMATICA
| For[n = 1, n < 100000, n++, If[IntegerQ[Sqrt[Sum[i*(i+1)/2, {i, n, n + 10}]]], Print[n]]] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 30 2006
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CROSSREFS
| Cf. A176541, A176542, A165517, A202391
Sequence in context: A010003 A007587 A034462 * A035340 A127305 A001662
Adjacent sequences: A116473 A116474 A116475 * A116477 A116478 A116479
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KEYWORD
| nonn
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AUTHOR
| Edward Fedorovich (chipramy(AT)012.net.il), Mar 29 2006
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EXTENSIONS
| Extended by Max Alekseyev (maxale(AT)gmail.com), Jan 20 2010
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