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A124820
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Expansion of (1-x)/(1-4*x+3*x^2-x^3).
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6
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1, 3, 9, 28, 88, 277, 872, 2745, 8641, 27201, 85626, 269542, 848491, 2670964, 8407925, 26467299, 83316385, 262271568, 825604416, 2598919345, 8181135700, 25753389181, 81069068969, 255197244033, 803335158406, 2528817970494
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OFFSET
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0,2
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COMMENTS
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Let M = a triangle with the triangular series in every column, but the leftmost column is shifted upwards one row. Then A124820 = Lim_{n->inf} M^n, the left-shifted vector considered as a sequence. - Gary W. Adamson, Jul 27 2010
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LINKS
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FORMULA
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a(n) = sum( k=0..n, C(n+2k+1, 3k+1) ).
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MATHEMATICA
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CoefficientList[Series[(1 - x)/(1 - 4 x + 3 x^2 - x^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jun 20 2014 *)
LinearRecurrence[{4, -3, 1}, {1, 3, 9}, 30] (* Harvey P. Dale, Apr 29 2016 *)
Table[Sum[Binomial[n + 2 k + 1, 3 k + 1], {k, 0, n}], {n, 0, 25}] (* Michael De Vlieger, Aug 03 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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