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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.
0
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
1,2
COMMENTS
The integer that is at the k-th row of the middle column of this pyramid of order n will be noted T(n,k).
Each row has n terms.
FORMULA
T(n,1) = n.
T(n,2) = 3n - 2.
T(n,3) = 9n - 8.
T(n,4) = 27n - 30.
T(n,5) = 81n - 104.
T(n,n) = A359087(n).
T(n,k) = 3^(k-1)*n - 2*A132894(k-1) for 1 <= k <= n (conjectured).
EXAMPLE
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
PROG
(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
CROSSREFS
Cf. A132894, A359087 (right diagonal).
Columns k=1..3: A000027, A016777, A017173.
Sequence in context: A333028 A296449 A309201 * A253792 A058330 A124256
KEYWORD
nonn,tabl
AUTHOR
Bernard Schott, Jan 27 2023
STATUS
approved