A110425 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 array by rows.

1, 2, 1, 3, 3, -3, 4, 5, 0, -14, 5, 7, 3, -10, -35, 6, 9, 6, -6, -30, -69, 7, 11, 9, -2, -25, -63, -119, 8, 13, 12, 2, -20, -57, -112, -188, 9, 15, 15, 6, -15, -51, -105, -180, -279, 10, 17, 18, 10, -10, -45, -98, -172, -270, -395, 11, 19, 21, 14, -5, -39, -91, -164, -261, -385, -539, 12, 21, 24, 18, 0, -33, -84, -156, -252

Offset

1,2

Links

Table of n, a(n) for n=1..75.

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
Sequence contains the array by rows.

Prog

;; PLT DrScheme (Zucker)
(define (triangle n) (* n (add1 n) 1/2))
(define (A110425 n)
(build-list n (lambda (r) (- (triangle (- n (triangle r)))
(triangle (- n (triangle (add1 r))))))))

Crossrefs

Cf. A110426, A110427.

Sequence in context: A085599 A299966 A302395 * A174257 A105637 A029161

Adjacent sequences: A110422 A110423 A110424 * A110426 A110427 A110428

Keyword

easy,sign,tabl

Author

Amarnath Murthy, Aug 01 2005

Extensions

More terms from Joshua Zucker, May 10 2006

Status

approved