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A154293
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Integers of the form : 1/6+2/6+3/6+4/6+5/6+....
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18
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0, 1, 6, 11, 13, 20, 35, 46, 50, 63, 88, 105, 111, 130, 165, 188, 196, 221, 266, 295, 305, 336, 391, 426, 438, 475, 540, 581, 595, 638, 713, 760, 776, 825, 910, 963, 981, 1036, 1131, 1190, 1210, 1271, 1376, 1441, 1463, 1530, 1645, 1716, 1740, 1813, 1938, 2015
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| 1/6+2/6+3/6=1, 1/6+2/6+3/6+4/6+5/6+6/6+7/6+8/6=6,...
a(n) is the set of all integers k such that 48k+1 is a perfect square. The square roots of 48*a(n)+1 = 1,7,17,23,25... = 8*(n-floor(n/4))+(-1)^n [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 01 2010]
Conjecture: even generalized pentagonal numbers (A193828) divided by 2. - Omar E. Pol, Aug 19 2011
The above conjecture is correct. [Charles R Greathouse IV, Jan 02 2012]
Quasipolynomial of order 4. [Charles R Greathouse IV, Jan 02 2012]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-5,7,-7,5,-3,1).
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FORMULA
| a(n) = A000217(A108752(n))/6. Conjecture: G.f. x(x^2-x+1)(x^2+4x+1)/((1+x^2)^2*(1-x)^3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 07 2009]
The conjecture is correct. [Charles R Greathouse IV, Jan 02 2012]
a(n)=(f(n)^2-1)/48 where f(n) = 8*(n-floor(n/4))+(-1)^n..with offset 0..a(O)=0 [From Gary Detlefs (gdetlefs(AT)aol.com), Mar 01 2010]
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MAPLE
| f:=n-> 8*(n-floor(n/4))+(-1)^n:seq((f(n)^2-1)/48, n=0..51); # From Gary Detlefs (gdetlefs(AT)aol.com), Mar 01 2010
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MATHEMATICA
| lst={}; s=0; Do[s+=n/6; If[Floor[s]==s, AppendTo[lst, s]], {n, 0, 7!}]; lst (* Orlovsky *)
Select[Table[Plus@@Range[n]/6, {n, 200}], IntegerQ] (* Alonso del Arte, Jan 20 2012 *)
LinearRecurrence[{3, -5, 7, -7, 5, -3, 1}, {0, 1, 6, 11, 13, 20, 35}, 60] (* Charles R Greathouse IV, Jan 20 2012 *)
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PROG
| (PARI) a(n)=n--; (8*(n-n\4)+(-1)^n)^2\48 \\ Charles R Greathouse IV, Jan 02 2012
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CROSSREFS
| Cf. A001318, A074378, A057569, A057570, A154292.
Sequence in context: A046953 A121765 A102974 * A199717 A068308 A163871
Adjacent sequences: A154290 A154291 A154292 * A154294 A154295 A154296
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KEYWORD
| nonn,easy
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Jan 06 2009
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