A124572 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 (1,3,1,3,1,3,...) on its main diagonal and (3,1,3,1,3,1,...) on its superdiagonal.

1, 1, 3, 1, 12, 3, 1, 39, 15, 9, 1, 120, 54, 72, 9, 1, 363, 174, 378, 81, 27, 1, 1092, 537, 1656, 459, 324, 27, 1, 3279, 1629, 6579, 2115, 2349, 351, 81, 1, 9840, 4908, 24624, 8694, 13392, 2700, 1296, 81, 1, 29523, 14748, 88596, 33318, 66258, 16092

Offset

0,3

Comments

Diagonal terms are switched to generate A124573. The row sum of row n is 4^n.

Links

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

Example

Row 3 = [1, 39, 15, 9] since when n = 3 we have M^3 = [[1, 39, 15, 9], [0, 27, 13, 21], [0, 0, 1, 39], [0, 0, 0, 27]]. The first few rows of the triangle are:
  1;
  1,   3;
  1,  12,   3;
  1,  39,  15,   9;
  1, 120,  54,  72,  9;
  1, 363, 174, 378, 81, 27;
  ...

Maple

with (LinearAlgebra): for n from 0 to 10 do M := Matrix (n+1, (i, j)->`if`(i=j and i mod 2 = 1, 1, `if`(i=j, 3, `if`(i=j-1 and i mod 2 = 1, 3, `if`(i=j-1, 1, 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. A124573, A124730, A124731, A029858 (column 2).

Sequence in context: A287197 A118020 A178619 * A144880 A144881 A121420

Adjacent sequences: A124569 A124570 A124571 * A124573 A124574 A124575

Keyword

nonn,easy,tabl

Author

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

Status

approved