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Search: id:A102001
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| A102001 |
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A weighted tribonacci, (1,2,4). |
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+0
4
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| 1, 3, 9, 19, 49, 123, 297, 739, 1825, 4491, 11097, 27379, 67537, 166683, 411273, 1014787, 2504065, 6178731, 15246009, 37619731, 92826673, 229050171, 565182441
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OFFSET
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1,2
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COMMENT
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A102000 is generated from a 4X4 matrix, same format. A102002 is another recursive (1,2,4) sequence, generated from the matrix [0 1 0 / 0 0 1 / 4 2 1]. a(n)/a(n-1) tends to 2.46750385...an eigenvalue of M and a root of the characteristic polynomial x^3 - x^2 - 2x - 4.
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FORMULA
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a(n) = a(n-1) + 2*a(n-2) + 4*a(n-3), n>3. a(n) = left term in M^n * [1 0 0], where M = the 3X3 matrix [1 1 1 / 2 0 0 / 0 2 0].
a(n)=sum{k=0..n, T(n-k, k)2^k}, T(n, k) = trinomial coefficients (A027907). - Paul Barry (pbarry(AT)wit.ie), Feb 15 2005
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EXAMPLE
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a(6) = 123 since M^6 * [1 0 0] = [123 98 76].
a(6) = 123 = 49 + 2*19 + 4*9 = a(5) + 2*a(4) + 4*a(3).
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CROSSREFS
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Sequence in context: A028377 A147439 A091411 this_sequence A146901 A147477 A146677
Adjacent sequences: A101998 A101999 A102000 this_sequence A102002 A102003 A102004
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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), Dec 23 2004
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