OFFSET
1,4
EXAMPLE
Illustration of a(16) = 38 in two ways:
.
Level
1
2 _ _
3 |_| _|_|
4 _|_| _|_|
5 |_ _| _|_ _|
6 _|_| _|_|
7 |_ _| _|_ _|
8 _|_ _| _|_ _|
9 |_ _| _ _|_ _|
10 _|_ _| |_| _|_ _|_|
11 |_ _ _| |_| _|_ _ _|_|
12 _|_ _| |_| _|_ _|_|
13 |_ _ _| _|_| _|_ _ _|_|
14 _|_ _ _| |_ _| _|_ _ _|_ _|
15 |_ _ _| |_| _|_ _ _|_|
16 |_ _ _| |_| |_ _ _|_|
...
Figure 1. Figure 2.
.
For n = 16, figure 1 shows the illustration of a(16) taken from the isosceles triangle of A237593. There are 38 cells in the first 16 levels of the diagram, so a(16) = 38.
PROG
(PARI) row235791(n) = vector((sqrtint(8*n+1)-1)\2, i, 1+(n-(i*(i+1)/2))\i);
row237591(n) = {my(orow = concat(row235791(n), 0)); vector(#orow -1, i, orow[i] - orow[i+1]); }
a003056(n) = floor((sqrt(1+8*n)-1)/2);
a322141(n) = my(row=row237591(n)); sum(k=1, a003056(n), if (!(k%2), row[k]));
a(n) = sum(k=1, n, a322141(k)); \\ Michel Marcus, Dec 22 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Dec 21 2020
STATUS
approved