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A118729
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Infinite square array which contains the 8 numbers 4*r^2 - 3*r, 4*r^2 - 2*r, ..., 4*r^2 + 4*r in row r.
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14
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0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 42, 45, 48, 52, 56, 60, 64, 68, 72, 76, 80, 85, 90, 95, 100, 105, 110, 115, 120, 126, 132, 138, 144, 150, 156, 162, 168
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OFFSET
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0,10
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COMMENTS
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The numbers in row r span the interval ]8*A000217(r-1), 8*A000217(r)].
The first difference between the entries in row r is r.
Partial sums of floor(n/8). - Philippe Deléham, Mar 26 2013
Apart from the initial zeros, the same as A008726. - Philippe Deléham, Mar 28 2013
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,1,-2,1).
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FORMULA
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From Philippe Deléham, Mar 26 2013: (Start)
a(8k) = A001107(k).
a(8k+1) = A002939(k).
a(8k+2) = A033991(k).
a(8k+3) = A016742(k).
a(8k+4) = A007742(k).
a(8k+5) = A002943(k).
a(8k+6) = A033954(k).
a(8k+7) = A033996(k). (End)
G.f.: x^8/(((1-x)^2*(1-x^8)). - Philippe Deléham, Mar 28 2013
a(n) = floor(n/8)*(n-3-4*floor(n/8)). - Ridouane Oudra, Jun 04 2019
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EXAMPLE
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The array starts in row r=0 as
.0..0..0..0..0..0..0..0;
.1..2..3..4..5..6..7..8;
10.12.14.16.18.20.22.24;
27.30.33.36.39.42.45.48;
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MATHEMATICA
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Flatten[Table[4r^2+r(Range[-3, 4]), {r, 0, 6}]] (* or *) LinearRecurrence[ {2, -1, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, 60] (* Harvey P. Dale, Nov 26 2015 *)
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CROSSREFS
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Cf. similar sequences: A000217, A002620, A130518, A130519, A130520, A174709, A174738, A218470, A131242.
Sequence in context: A113768 A122936 A330729 * A008726 A302834 A022788
Adjacent sequences: A118726 A118727 A118728 * A118730 A118731 A118732
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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Stuart M. Ellerstein (ellerstein(AT)aol.com), May 21 2006
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EXTENSIONS
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Redefined as a square tabf array and description simplified by R. J. Mathar, Oct 20 2010
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STATUS
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approved
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