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%I #18 May 27 2017 14:54:16
%S 1,3,3,-5,-30,-84,-182,-342,-585,-935,-1419,-2067,-2912,-3990,-5340,
%T -7004,-9027,-11457,-14345,-17745,-21714,-26312,-31602,-37650,-44525,
%U -52299,-61047,-70847,-81780,-93930,-107384,-122232,-138567,-156485,-176085,-197469,-220742,-246012,-273390,-302990
%N 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.
%H Colin Barker, <a href="/A110426/b110426.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F 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
%F a(n) = A000330(n) - A000914(n-1). - _J. M. Bergot_, May 27 2017
%F From _Colin Barker_, May 27 2017: (Start)
%F G.f.: x*(1 - 2*x - 2*x^2) / (1 - x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F (End)
%e 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 e.g. the row corresponding to 4 contains
%e 4, (3+2),{(1) +(0)+(-1)}, {(-2)+(-3)+(-4)+(-5)} ----> 4,5,0,-14
%e 1
%e 2 1
%e 3 3 -3
%e 4 5 0 -14
%e 5 7 3 -10 -35
%e 6 9 6 -6 -30 -69
%e ...
%e Sequence contains the row sums.
%o ;;PLT DrScheme (Zucker)
%o (apply + (A110425 n))
%o ;;see A110425 for definition of that function.
%o (PARI) Vec(x*(1 - 2*x - 2*x^2) / (1 - x)^5 + O(x^50)) \\ _Colin Barker_, May 27 2017
%Y Cf. A110425, A110427.
%K easy,sign
%O 1,2
%A _Amarnath Murthy_, Aug 01 2005
%E More terms from _Joshua Zucker_, May 10 2006
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