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
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
KEYWORD
easy,sign
AUTHOR
Amarnath Murthy, Aug 01 2005
EXTENSIONS
More terms from Joshua Zucker, May 10 2006
STATUS
approved