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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. 4
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

Table of n, a(n) for n=1..43.

FORMULA

a(n)=n*(1+2n-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). [From R. J. Mathar, Jul 10 2009]

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 * A128916 A130287 A167858

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 May 25 14:08 EDT 2017. Contains 287038 sequences.