A288842 Triangle (sans apex) of coefficients of terms of the form (eM_1)^j*(eM_2)^k re construction of triangle A287768.

1, 2, 3, 9, 6, 9, 36, 45, 18, 27, 135, 243, 189, 54, 81, 486, 1134, 1296, 729, 162, 243, 1701, 4860, 7290, 6075, 2673, 486, 729, 5832, 19683, 36450, 40095, 26244, 9477, 1458, 2187, 19683, 76545, 168399, 229635, 199017, 107163, 32805, 4374, 6561, 65610, 288684, 734832, 1194102, 1285956, 918540, 419904, 111537, 13122

Offset

1,2

Links

Table of n, a(n) for n=1..54.

G. G. Wojnar, D. Sz. Wojnar, and L. Q. Brin, Universal Peculiar Linear Mean Relationships in All Polynomials, Table GW.n=3, p.22, arXiv:1706.08381 [math.GM], 2017.

Formula

T(n+1,k+1) = 3*T(n,k) + 3*T(n,k+1).

Example

Triangle begins:
  1,  2;
  3,  9,  6;
  9, 36, 45, 18;

Mathematica

T[1, 1] = 1; T[1, 2] = 2;
T[n_, k_] /; 1 <= k <= n+1 := T[n, k] = 3 T[n-1, k-1] + 3 T[n-1, k];
T[_, _] = 0;
Table[T[n, k], {n, 1, 9}, {k, 1, n+1}] // Flatten (* Jean-François Alcover, Nov 16 2018 *)

Crossrefs

Columns are: A000244, A288834, A288835, A288836, A288838, etc.

Cf. A287768.

Sequence in context: A168221 A011028 A224519 * A108694 A267896 A199858

Adjacent sequences: A288839 A288840 A288841 * A288843 A288844 A288845

Keyword

nonn,tabf

Author

Gregory Gerard Wojnar, Jun 17 2017

Status

approved