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A124573
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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.
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2
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Companion triangle A124572 is generated by switching the main diagonal with the superdiagonal. The row sum of row n is 4^n.
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..5000
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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;
...
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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
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CROSSREFS
| Cf. A124572, A124730, A124731, A000244 (column 1), A003462 (column 2).
Sequence in context: A067417 A187887 A016577 * A127550 A021317 A091579
Adjacent sequences: A124570 A124571 A124572 * A124574 A124575 A124576
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Nov 04 2006
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