A124573 Triangle read by rows where the n-th row is the first row of M^n, with M the (n+1)-by-(n+1) matrix with (3,1,3,1,3,1,...) on its main diagonal and (1,3,1,3,1,3,...) on its superdiagonal.

1, 3, 1, 9, 4, 3, 27, 13, 21, 3, 81, 40, 102, 24, 9, 243, 121, 426, 126, 99, 9, 729, 364, 1641, 552, 675, 108, 27, 2187, 1093, 6015, 2193, 3681, 783, 405, 27, 6561, 3280, 21324, 8208, 17622, 4464, 3564, 432, 81, 19683, 9841, 73812, 29532, 77490, 22086

Offset

0,2

Comments

Companion triangle A124572 is generated by switching the main diagonal with the superdiagonal. The row sum of row n is 4^n.

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..5000

Example

Row 3 = [27, 13, 21, 3] since when n = 3 we have M^3 = [[27, 13, 21, 3], [0, 1, 39, 15], [0, 0, 27, 13], [0, 0, 0, 1]].
First few rows of the triangle are:
    1;
    3,   1;
    9,   4,   3;
   27,  13,  21,   3;
   81,  40, 102,  24,  9;
  243, 121, 426, 126, 99, 9;
  ...

Maple

with (LinearAlgebra): for n from 0 to 10 do M := Matrix (n+1, (i, j)->`if`(i=j and i mod 2 = 1, 3, `if`(i=j, 1, `if`(i=j-1 and i mod 2 = 1, 1, `if`(i=j-1, 3, 0))))): X := M^n: for m from 0 to n do printf("%d, ", X[1, m+1]): od: od: # Nathaniel Johnston, Apr 28 2011

Crossrefs

Cf. A124572, A124730, A124731, A000244 (column 1), A003462 (column 2).

Sequence in context: A016577 A308704 A270702 * A127550 A021317 A091579

Adjacent sequences: A124570 A124571 A124572 * A124574 A124575 A124576

Keyword

nonn,easy,tabl

Author

Gary W. Adamson & Roger L. Bagula, Nov 04 2006

Status

approved