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%I #8 Oct 07 2015 08:37:05
%S 1,7,23,57,118,218,370,590,895,1305,1841,2527,3388,4452,5748,7308,
%T 9165,11355,13915,16885,20306,24222,28678,33722,39403,45773,52885,
%U 60795,69560,79240,89896,101592,114393,128367,143583,160113,178030,197410,218330,240870
%N Areas of a sequence of right-angled figures described below.
%C From the NW corner to the SE corner, going the upper (or right) way, the edges have lengths n, n-1, ..., 2, 1, 1, 2, ..., n-1, n. Going the lower (or left) way, the edges have lengths n,1,n-1,2,...,2,n-1,1,n.
%H Colin Barker, <a href="/A058195/b058195.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,0,5,-4,1).
%F a(n) = [(2n^4+10n^3+13n^2+2n)/24], where [] denotes floor. (For even n there is no need for truncation. For odd n the [] removes 1/8.) A formula without [] is (4n^4+20n^3+26n^2+4n+3+3(-1)^(n+1))/48.
%F From _Colin Barker_, Oct 07 2015: (Start)
%F a(n) = 4*a(n-1)-5*a(n-2)+5*a(n-4)-4*a(n-5)+a(n-6) for n>6.
%F a(n) = (2*n^4+10*n^3+13*n^2+2*n)/24 for n even.
%F a(n) = (2*n^4+10*n^3+13*n^2+2*n-3)/24 for n odd.
%F G.f.: -x*(3*x+1) / ((x-1)^5*(x+1)).
%F (End)
%e For n=6 the figure is (assuming the "#" character is square ...):
%e ######
%e ######
%e ######
%e ######
%e ######
%e ##########
%e .#########
%e .#########
%e .###########
%e .############
%e .############
%e ...#############
%e ...#############
%e ...#############
%e ...#############
%e ......###############
%e ......###############
%e ......###############
%e ..........###########
%e ..........###########
%e ...............######
%o (PARI) Vec(-x*(3*x+1)/((x-1)^5*(x+1)) + O(x^100)) \\ _Colin Barker_, Oct 07 2015
%K easy,nonn
%O 1,2
%A _Jonas Wallgren_, Nov 26 2000
%E More terms from _James A. Sellers_, Dec 06 2000
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