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A022276
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a(n) = n*(19*n - 1)/2.
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3
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0, 9, 37, 84, 150, 235, 339, 462, 604, 765, 945, 1144, 1362, 1599, 1855, 2130, 2424, 2737, 3069, 3420, 3790, 4179, 4587, 5014, 5460, 5925, 6409, 6912, 7434, 7975, 8535, 9114, 9712, 10329, 10965, 11620, 12294, 12987, 13699, 14430, 15180, 15949, 16737, 17544, 18370
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 19*n + a(n-1) - 10 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010
From Vincenzo Librandi, Mar 31 2015: (Start)
G.f.: x*(9 + 10*x)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. (End)
a(n) = A022277(-n). - Bruno Berselli, Apr 01 2015
a(n) = A000217(10*n-1) - A000217(9*n-1). - Bruno Berselli, Oct 17 2016
E.g.f.: (x/2)*(19*x + 18)*exp(x). - G. C. Greubel, Aug 23 2017
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MATHEMATICA
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Table[n (19 n - 1)/2, {n, 0, 40}] (* Bruno Berselli, Mar 12 2015 *)
CoefficientList[Series[x (9 + 10 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 31 2015 *)
LinearRecurrence[{3, -3, 1}, {0, 9, 37}, 50] (* Harvey P. Dale, Jul 25 2021 *)
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PROG
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(MAGMA) [n*(19*n - 1)/2: n in [0..45]]; // Vincenzo Librandi, Mar 31 2015
(PARI) a(n)=n*(19*n-1)/2 \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Cf. A000217, A022277.
Cf. similar sequences listed in A022288.
Sequence in context: A153244 A200774 A273220 * A171443 A341403 A320696
Adjacent sequences: A022273 A022274 A022275 * A022277 A022278 A022279
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Vincenzo Librandi, Mar 31 2015
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STATUS
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approved
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