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 A118729 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. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS 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 LINKS 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). FORMULA 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 EXAMPLE 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; MATHEMATICA 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 *) CROSSREFS 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 KEYWORD nonn,tabf,easy AUTHOR Stuart M. Ellerstein (ellerstein(AT)aol.com), May 21 2006 EXTENSIONS Redefined as a square tabf array and description simplified by R. J. Mathar, Oct 20 2010 STATUS approved

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Last modified April 11 18:59 EDT 2021. Contains 342888 sequences. (Running on oeis4.)