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Search: id:A105038
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| A105038 |
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Nonnegative n such that 6*n^2 + 6*n + 1 is a square. |
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+0
6
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| 0, 4, 44, 440, 4360, 43164, 427284, 4229680, 41869520, 414465524, 4102785724, 40613391720, 402031131480, 3979697923084, 39394948099364, 389969783070560, 3860302882606240, 38213059042991844, 378270287547312204
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Conjectures: For n>0, a(n) = sqrt(6*a(n-1)^2 + 6*a(n-1) + 1)*4 + a(n-2). If this sequence is extended backwards indefinitely as follows: ...,4229680,427284,43164,4360,440,44,4,0,0,4,44,440,4360,43164,427284,4229680,... then the following recurrences hold for all n: a(n) = 10*a(n-1) - a(n-2) + 4, a(n) = 10*a(n+1) - a(n+2) + 4 and so 10*(a(n+1) - a(n-1)) = a(n-2) - a(n+2). a(n)^2 + a(n) = ((a(n+1) - a(n-1))^2/16 - 1)/6. There is a similar pattern for other values besides 6.
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FORMULA
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G.f.: 4*x/(1-11*x+11*x^2-x^3)
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PROGRAM
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(PARI) for(n=0, 427284, if(issquare(6*n*(n+1)+1), print1(n, ", ")))
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CROSSREFS
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Cf. A001652, A001570, A049629, A105040, A104240, A077288, A105036, A103200, A105037.
Equals (A072256(n+1) - 1)/2.
Sequence in context: A030987 A043039 A002754 this_sequence A002278 A112897 A163013
Adjacent sequences: A105035 A105036 A105037 this_sequence A105039 A105040 A105041
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KEYWORD
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nonn
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AUTHOR
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Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Apr 03 2005
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 05 2005
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