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

1,2

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.

Links

Table of n, a(n) for n=1..66.

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

Adjacent sequences: A360142 A360143 A360144 * A360146 A360147 A360148

Keyword

nonn,tabl

Author

Bernard Schott, Jan 27 2023

Status

approved