A360145 - OEIS

%I #27 Feb 01 2023 08:19:20

%S 1,2,4,3,7,19,4,10,28,78,5,13,37,105,301,6,16,46,132,382,1108,7,19,55,

%T 159,463,1351,3951,8,22,64,186,544,1594,4680,13758,9,25,73,213,625,

%U 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

%N 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.

%C 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).

%C Each row has n terms.

%F T(n,1) = n.

%F T(n,2) = 3n - 2.

%F T(n,3) = 9n - 8.

%F T(n,4) = 27n - 30.

%F T(n,5) = 81n - 104.

%F T(n,n) = A359087(n).

%F T(n,k) = 3^(k-1)*n - 2*A132894(k-1) for 1 <= k <= n (conjectured).

%e Triangle begins:

%e    n=1:  1;

%e    n=2:  2,  4;

%e    n=3:  3,  7, 19;

%e    n=4:  4, 10, 28,  78;

%e    n=5:  5, 13, 37, 105, 301;

%e    n=6:  6, 16, 46, 132, 382, 1108;

%e    ...

%e For n=5, the reverse pyramid summation is as follows and row 5 here is the middle column 5,13,37,...

%e   1    2    3    4    5    4    3    2    1

%e        6    9   12   13   12    9    6

%e            27   34   37   34   27

%e                 98  105   98

%e                     301

%o (PARI) f(v) = if (#v == 1, v, vector(#v-2, i, v[i]+v[i+1]+v[i+2]));

%o 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

%Y Cf. A132894, A359087 (right diagonal).

%Y Columns k=1..3: A000027, A016777, A017173.

%K nonn,tabl

%O 1,2

%A _Bernard Schott_, Jan 27 2023