A110426 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 row sums.

1, 3, 3, -5, -30, -84, -182, -342, -585, -935, -1419, -2067, -2912, -3990, -5340, -7004, -9027, -11457, -14345, -17745, -21714, -26312, -31602, -37650, -44525, -52299, -61047, -70847, -81780, -93930, -107384, -122232, -138567, -156485, -176085, -197469, -220742, -246012, -273390, -302990

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = sum_{i=(2-n)*(n+1)/2..n} i = (-n^4 + 2*n^3 + 5*n^2 + 2*n)/8. - Theresa Guinard, Nov 15 2013

a(n) = A000330(n) - A000914(n-1). - J. M. Bergot, May 27 2017

From Colin Barker, May 27 2017: (Start)

G.f.: x*(1 - 2*x - 2*x^2) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(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 row sums.

Prog

;; PLT DrScheme (Zucker)
(apply + (A110425 n))
;; see A110425 for definition of that function.
(PARI) Vec(x*(1 - 2*x - 2*x^2) / (1 - x)^5 + O(x^50)) \\ Colin Barker, May 27 2017

Crossrefs

Cf. A110425, A110427.

Sequence in context: A366594 A265878 A201496 * A200562 A093310 A256402

Adjacent sequences: A110423 A110424 A110425 * A110427 A110428 A110429

Keyword

easy,sign

Author

Amarnath Murthy, Aug 01 2005

Extensions

More terms from Joshua Zucker, May 10 2006

Status

approved