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A124572
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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 (1,3,1,3,1,3...) on its main diagonal and (3,1,3,1,3,1...) on its superdiagonal.
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2
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Diagonal terms are switched to generate A124573. 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 = [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;
...
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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, 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
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CROSSREFS
| Cf. A124573, A124730, A124731, A029858 (column 2).
Sequence in context: A048522 A118020 A178619 * A144880 A144881 A121420
Adjacent sequences: A124569 A124570 A124571 * A124573 A124574 A124575
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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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