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%I #4 Jun 06 2021 03:15:41
%S 0,1,2,7,10,22,28,50,60,95,100,131,122,152,130,162,128,165,120,165,
%T 200,226,242,252,250,247,228,215,180,260,300,356,362,397,370,387,328,
%U 330,240,330,400,451,482,497,490,472,428,380,300,425,500,581,602,642,610,612,528,495,360
%N Total area of all i X j rectangles where i and j are the final digits of positive integers r and s such that r + s = n.
%F a(n) = Sum_{k=1..floor(n/2)} (k mod 10) * ((n-k) mod 10).
%e a(20) = 165; There are 10 ways to write 20 as the sum of two positive integers: (19,1), (18,2), (17,3), (16,4), (15,5), (14,6), (13,7), (12,8), (11,9), and (10,10). Using the final digits from each pair as the side lengths of the rectangles, the combined area is 9*1 + 8*2 + 7*3 + 6*4 + 5*5 + 4*6 + 3+7 + 2*8 + 1*9 + 0*0 = 165.
%t Table[Sum[Mod[k, 10]*Mod[n - k, 10], {k, Floor[n/2]}], {n, 60}]
%Y Cf. A010879, A023855.
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, Jun 06 2021
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