|
| |
|
|
A014107
|
|
a(n) = n*(2*n-3).
|
|
32
|
|
|
|
0, -1, 2, 9, 20, 35, 54, 77, 104, 135, 170, 209, 252, 299, 350, 405, 464, 527, 594, 665, 740, 819, 902, 989, 1080, 1175, 1274, 1377, 1484, 1595, 1710, 1829, 1952, 2079, 2210, 2345, 2484, 2627, 2774, 2925, 3080, 3239, 3402, 3569, 3740, 3915, 4094, 4277
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Positive terms give a bisection of A000096. - Omar E. Pol, Dec 16 2016
|
|
|
LINKS
|
G. C. Greubel, Table of n, a(n) for n = 0..5000
Emily Barnard, Nathan Reading, Coxeter-biCatalan combinatorics, arXiv:1605.03524 [math.CO], 2016. See p. 51.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
|
|
|
FORMULA
|
a(n) = A033537(n) - 8*n^2; A100035(a(n)) = 2 for n > 1. - Reinhard Zumkeller, Oct 31 2004
A014106(-n) = a(n). - Michael Somos, Nov 06 2005
From Michael Somos, Nov 06 2005: (Start)
G.f.: x*(-1 + 5*x)/(1 - x)^3.
E.g.f: x*(-1 + 2*x)*exp(x). (End)
a(n) = A097070(n)/A000108(n - 2), n >= 2. - Philippe Deléham, Apr 12 2007
a(n) = 2*a(n-1) - a(n-2) + 4, n > 1; a(0) = 0, a(1) = -1, a(2) = 2. - Zerinvary Lajos, Feb 18 2008
a(n) = a(n-1) + 4*n - 5 with a(0) = 0. - Vincenzo Librandi, Nov 20 2010
a(n) = (2*n-1)*(n-1) - 1. Also, with an initial offset of -1, a(n) = (2*n-1)*(n+1) = 2*n^2 + n - 1. - Alonso del Arte, Dec 15 2012
(a(n) + 1)^2 + (a(n) + 2)^2 + ... + (a(n) + n)^2 = (a(n) + n + 1)^2 + (a(n) + n + 2)^2 + ... + (a(n) + 2n - 1)^2 starting with a(1) = -1. - Jeffreylee R. Snow, Sep 17 2013
|
|
|
MAPLE
|
A014107:=n->n*(2*n-3); seq(A014107(n), n=0..100); # Wesley Ivan Hurt, Nov 19 2013
|
|
|
MATHEMATICA
|
Table[2n^2 - 3n, {n, 0, 49}] (* Alonso del Arte, Dec 15 2012 *)
LinearRecurrence[{3, -3, 1}, {0, -1, 2}, 50] (* Harvey P. Dale, Sep 18 2018 *)
|
|
|
PROG
|
(PARI) a(n)=n*(2*n-3)
|
|
|
CROSSREFS
|
Cf. A100036, A100037, A100038, A100039.
a(n) = A100345(n, n - 3) for n > 2.
Sequence in context: A007115 A154495 A248121 * A173102 A090398 A091941
Adjacent sequences: A014104 A014105 A014106 * A014108 A014109 A014110
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
