Revision History for A235269
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#12 by Harvey P. Dale at Wed Oct 07 11:55:27 EDT 2015
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#11 by Harvey P. Dale at Wed Oct 07 11:55:21 EDT 2015
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| MATHEMATICA
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With[{nn=60}, Floor[Times@@#/Total[#]]&/@Thread[{Range[nn]^2, Accumulate[ Range[ nn]]}]] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 1, 3, 6, 9, 13, 17, 23, 28, 35, 42}, 60] (* Harvey P. Dale, Oct 07 2015 *)
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approved
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#10 by Charles R Greathouse IV at Sat Jun 13 00:54:56 EDT 2015
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<a href="/index/Rec#order_11">Index to sequencesentries withfor linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,1,-2,1).
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Discussion
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| Sat Jun 13
| 00:54
| OEIS Server: https://oeis.org/edit/global/2439
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#9 by R. J. Mathar at Thu Sep 25 05:04:33 EDT 2014
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#8 by R. J. Mathar at Thu Sep 25 05:04:19 EDT 2014
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<a href="/index/ReaRec#recLCCorder_11">Index to sequences with linear recurrences with constant coefficients</a>>, signature (2,-1,0,0,0,0,0,0,1,-2,1).
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approved
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#7 by Ralf Stephan at Wed Jan 15 05:14:17 EST 2014
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#6 by Ralf Stephan at Wed Jan 15 05:11:54 EST 2014
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| NAME
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floor(s*t/(s+t)), where s = (n^2) are the squares, t = triangular(n).) the triangular numbers.
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| LINKS
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<a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>
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| FORMULA
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G.f.: (-x^10 + 2*x^9 - x^8 + 2*x^7 + x^5 + x^3 + x^2 + x)/((1-x)^2*(1-x^9)). - Ralf Stephan, Jan 15 2014
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proposed
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Discussion
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| Wed Jan 15
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| Ralf Stephan: It's sufficiently simple to be included, as good as any linrec. For what is interesting, please see my opinion: http://unsexy-science.blogspot.com/2013/09/random-100-sequences-from-oeis-survey.html
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#5 by Alex Ratushnyak at Sun Jan 05 14:17:05 EST 2014
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Discussion
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| Mon Jan 06
| 03:43
| Joerg Arndt: Apparently has a rational g.f.; looks quite random to me, can you give a motivation?
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| Tue Jan 07
| 13:28
| Alex Ratushnyak: The motivation is to add the sequence to OEIS if editors find it worth adding, and otherwise to learn more about what sequences aren't worth.
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#4 by Alex Ratushnyak at Sun Jan 05 14:16:33 EST 2014
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| FORMULA
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a(n) = floor(s*t/(s+t)) = floor)) where s = A000290(n^3*(n+1)/2 / ((2*) = n^2+, t = A000217(n) = n*(n+1))/2)) = floor((n^4+n^3) / (3*n^)/2+. a(n)) = ) = floor( (((n^3+n^2) / (3*n+1)).
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#3 by Alex Ratushnyak at Sun Jan 05 14:13:30 EST 2014
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| FORMULA
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a(n) = floor(s*t/(s+t)) = floor(n^3*(n+1)/2 / ((2*n^2+n*(n+1))/2)) = floor((n^4+n^3) / (3*n^2+n)) = floor( (n^3+n^2) / (3*n+1)).
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| CROSSREFS
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Cf. A000217, A000290.
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