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A122709
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a(0)=1; thereafter a(n) = 9*n - 3.
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5
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1, 6, 15, 24, 33, 42, 51, 60, 69, 78, 87, 96, 105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 294, 303, 312, 321, 330, 339, 348, 357, 366, 375, 384, 393, 402, 411, 420, 429, 438, 447, 456, 465, 474, 483
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(0)=1, a(n) = 9*n - 3 = A008591(n) - 3 for n > 0.
a(n) = 2*a(n-1) - a(n-2) for n > 2; a(0)=1, a(1)=6, a(2)=15.
a(n) = a(n-1) + 9 for n > 1; a(0)=1, a(1)=6.
G.f.: ((1 + 2*x)/(1 - x))^2.
Equals binomial transform of [1, 5, 4, -4, 4, -4, 4, ...]. - Gary W. Adamson, Dec 10 2007
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MAPLE
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seq(coeff(series(((1+2*x)/(1-x))^2, x, n+1), x, n), n = 0 .. 60); # Muniru A Asiru, Oct 21 2018
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MATHEMATICA
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Join[{1}, LinearRecurrence[{2, -1}, {6, 15}, 60]] (* Harvey P. Dale, Jun 12 2012 *)
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PROG
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(PARI) Vec((1 + 2*x)^2 / (1 - x)^2 + O(x^100)) \\ Colin Barker, Jan 22 2018
(GAP) a:=[6, 15];; for n in [3..60] do a[n]:=2*a[n-1]-a[n-2]; od; Concatenation([1], a); # Muniru A Asiru, Oct 21 2018
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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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EXTENSIONS
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STATUS
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approved
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