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 A110427 The r-th term of the n-th row of the following array contains the sum of r successively decreasing integers beginning from n. 0 < r <= n. E.g., the row corresponding to 4 contains 4, (3+2),{(1) +(0)+(-1)}, {(-2)+(-3)+(-4)+(-5)} ----> 4,5,0,-14 1 2 1 3 3 -3 4 5 0 -14 5 7 3 -10 -35 6 9 6 -6 -30 -69 ... Sequence contains the leading diagonal. 5
 1, 1, -3, -14, -35, -69, -119, -188, -279, -395, -539, -714, -923, -1169, -1455, -1784, -2159, -2583, -3059, -3590, -4179, -4829, -5543, -6324, -7175, -8099, -9099, -10178, -11339, -12585, -13919, -15344, -16863, -18479, -20195, -22014, -23939, -25973, -28119, -30380, -32759, -35259, -37883 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS FORMULA From R. J. Mathar, Jul 10 2009: (Start) a(n) = n*(1 + 2*n - n^2)/2 = n - A002411(n-1). G.f.: x*(1 - 3*x - x^2)/(1-x)^4. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) EXAMPLE The r-th term of the n-th row of the following array contains the sum of r successively decreasing integers beginning from n. 0 < r <= n. E.g., the row corresponding to 4 contains 4, (3+2),{(1) +(0)+(-1)}, {(-2)+(-3)+(-4)+(-5)} ----> 4,5,0,-14 1 2 1 3 3 -3 4 5 0 -14 5 7 3 -10 -35 6 9 6 -6 -30 -69 ... Sequence contains the leading diagonal. MAPLE a:=n->sum(j*n-1, j=0..n):seq(-a(n), n=0..42); # Zerinvary Lajos, Feb 06 2007 seq(-sum(n^2-2, k=0..n)/2, n=0..42); # Zerinvary Lajos, Jan 28 2008 PROG ;; PLT DrScheme (Zucker) (first (reverse (A110425 n)) ;; see A110425 for definition of that function. CROSSREFS Cf. A110425, A110426. Sequence in context: A081379 A081377 A050934 * A296294 A128916 A130287 Adjacent sequences:  A110424 A110425 A110426 * A110428 A110429 A110430 KEYWORD easy,sign AUTHOR Amarnath Murthy, Aug 01 2005 EXTENSIONS More terms from Joshua Zucker, May 10 2006 STATUS approved

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Last modified April 17 08:40 EDT 2021. Contains 343064 sequences. (Running on oeis4.)