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Search: id:A094944
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| A094944 |
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A sequence with a(n)/a(n-1) converging to 7, generated from a semi-magic square. |
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+0
2
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| 1, 17, 121, 769, 5681, 39121, 274345, 1922945, 13447009, 94165777, 659108825, 4613711233, 32296542097, 226073894609, 1582520918281, 11077645104385, 77543495432897, 542804558486545, 3799631689665337, 26597422073425409
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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3 rows: 1 4 2, 2 1 4, 4 2 1 form a semi-magic square: row sums and columns and the diagonal = 7, the convergent of the sequence.
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FORMULA
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Let M = the 3 X 3 matrix [1 4 2 / 2 1 4 / 4 2 1], then with M^n * [1 0 0] = [p q r], a(n) = p.
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EXAMPLE
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a(4) = 769 since M^4 * [1 0 0] = [769 824 808].
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MATHEMATICA
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a[n_] := (MatrixPower[{{1, 4, 2}, {2, 1, 4}, {4, 2, 1}}, n].{{1}, {0}, {0}})[[1, 1]]; Table[ a[n], {n, 10}] (from Robert G. Wilson v May 29 2004)
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CROSSREFS
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Cf. A094943 uses the same format and operations but with different terms.
Sequence in context: A048714 A010823 A022709 this_sequence A108682 A031213 A021003
Adjacent sequences: A094941 A094942 A094943 this_sequence A094945 A094946 A094947
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), May 25 2004
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), May 29 2004
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