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%I #46 Dec 23 2020 17:18:34
%S 1,3,5,8,11,16,21,27,34,41,48,57,66,75,86,98,110,123,136,151,166,181,
%T 196,213,231,249,267,287,307,329,351,374,397,420,445,471,497,523,549,
%U 577,605,635,665,695,727,759,791,825,860,896,932,968,1004,1042,1080,1120,1160,1200,1240,1282
%N a(n) is the sum of odd-indexed terms (of every row) of the first n rows of the triangle A237591.
%H Michel Marcus, <a href="/A338204/b338204.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = A000217(n) - A338758(n).
%e Illustration of a(16) = 98 in two ways:
%e .
%e Level _ _
%e 1 _|_| |_|_
%e 2 _|_ _| |_ _|
%e 3 _|_ _| |_ _|_
%e 4 _|_ _ _| |_ _ _|
%e 5 _|_ _ _| _ |_ _ _|_ _
%e 6 _|_ _ _ _| |_| |_ _ _ _|_|
%e 7 _|_ _ _ _| |_| |_ _ _ _|_|_
%e 8 _|_ _ _ _ _| _|_| |_ _ _ _ _|_|_
%e 9 _|_ _ _ _ _| |_ _| |_ _ _ _ _|_ _|
%e 10 _|_ _ _ _ _ _| |_| |_ _ _ _ _ _|_|
%e 11 _|_ _ _ _ _ _| _|_| |_ _ _ _ _ _|_|_ _
%e 12 _|_ _ _ _ _ _ _| |_ _| |_ _ _ _ _ _ _|_ _|
%e 13 _|_ _ _ _ _ _ _| |_ _| |_ _ _ _ _ _ _|_ _|
%e 14 _|_ _ _ _ _ _ _ _| _|_| _ |_ _ _ _ _ _ _ _|_|_ _
%e 15 _|_ _ _ _ _ _ _ _| |_ _| |_| |_ _ _ _ _ _ _ _|_ _|_|_
%e 16 |_ _ _ _ _ _ _ _ _| |_ _| |_| |_ _ _ _ _ _ _ _ _|_ _|_|
%e ...
%e Figure 1. Figure 2.
%e .
%e For n = 16, figure 1 shows the illustration of a(16) taken from the isosceles triangle of A237593. There are 98 cells in the first 16 rows of the diagram, so a(16) = 98.
%e Figure 2 shows the illustration of a(16) taken from an octant of the pyramid described in A244050 and A245092. There are 98 cells in the first 16 rows of the diagram, so a(16) = 98.
%o (PARI) row235791(n) = vector((sqrtint(8*n+1)-1)\2, i, 1+(n-(i*(i+1)/2))\i);
%o row237591(n) = {my(orow = concat(row235791(n), 0)); vector(#orow -1, i, orow[i] - orow[i+1]); }
%o a003056(n) = floor((sqrt(1+8*n)-1)/2);
%o f(n) = my(row=row237591(n)); sum(k=1, a003056(n), if ((k%2), row[k])); \\ A240542
%o a(n) = sum(k=1, n, f(k)); \\ _Michel Marcus_, Dec 22 2020
%Y Partial sums of A240542.
%Y Cf. A000217, A067742, A235791, A237591, A237593, A259176, A286001, A322141, A338758.
%K nonn
%O 1,2
%A _Omar E. Pol_, Dec 21 2020
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