A360145 Triangle read by rows where row n is the largest (or middle or n-th) column of the reverse pyramid summation of order n described in A359087.
1, 2, 4, 3, 7, 19, 4, 10, 28, 78, 5, 13, 37, 105, 301, 6, 16, 46, 132, 382, 1108, 7, 19, 55, 159, 463, 1351, 3951, 8, 22, 64, 186, 544, 1594, 4680, 13758, 9, 25, 73, 213, 625, 1837, 5409, 15945, 47049, 10, 28, 82, 240, 706, 2080, 6138, 18132, 53610, 158616, 11, 31, 91, 267, 787, 2323, 6867, 20319, 60171, 178299, 528619
Offset: 1
Examples
Triangle begins:
n=1: 1;
n=2: 2, 4;
n=3: 3, 7, 19;
n=4: 4, 10, 28, 78;
n=5: 5, 13, 37, 105, 301;
n=6: 6, 16, 46, 132, 382, 1108;
...
For n=5, the reverse pyramid summation is as follows and row 5 here is the middle column 5,13,37,...
1 2 3 4 5 4 3 2 1
6 9 12 13 12 9 6
27 34 37 34 27
98 105 98
301
Programs
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PARI
f(v) = if (#v == 1, v, vector(#v-2, i, v[i]+v[i+1]+v[i+2])); row(n) = my(u = concat([1..n], Vecrev([1..n-1])), v=u, w = vector(n)); for (i=1, n, w[i] = v[#v\2+1]; v = f(v);); w; \\ Michel Marcus, Jan 30 2023
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