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Search: id:A095311
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| 1, 47, 138, 274, 455, 681, 952, 1268, 1629, 2035, 2486, 2982, 3523, 4109, 4740, 5416, 6137, 6903, 7714, 8570, 9471, 10417, 11408, 12444, 13525, 14651, 15822, 17038, 18299, 19605, 20956, 22352, 23793, 25279, 26810, 28386, 30007, 31673, 33384
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OFFSET
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1,2
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REFERENCES
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Albert H. Beiler, "Recreations in the Theory of Numbers", Dover, 1966, p. 185-194.
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FORMULA
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a(n+3) = 3*a(n+2) - 3*a(n+1) - a(n); a(1) = 1, a(2) = 47, a(3) = 138. Let M = the 3 X 3 matrix [1 0 0 / 1 1 0 / 1 45 1]. Then M^n * [1 0 0] = [1 n a(n)].
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EXAMPLE
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a(6) = 681 = 3*a(5) - 3*a(4) + a(3) = 3*455 - 3*274 + 138.
a(37) = 30007 since M^37 * [1 0 0] = [1 37 30007].
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MATHEMATICA
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a[n_] := (MatrixPower[{{1, 0, 0}, {1, 1, 0}, {1, 45, 1}}, n].{{1}, {0}, {0}})[[3, 1]]; Table[ a[n], {n, 40}] (from Robert G. Wilson v Jun 05 2004)
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CROSSREFS
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Cf. A081422, A000326, A000384, A000566, A000567... etc. (all polygonal sequences).
Sequence in context: A044298 A044679 A039530 this_sequence A005112 A062637 A040984
Adjacent sequences: A095308 A095309 A095310 this_sequence A095312 A095313 A095314
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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), Jun 02 2004
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 05 2004
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