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A172043
a(n) = 5*n^2 - n + 1.
4
1, 5, 19, 43, 77, 121, 175, 239, 313, 397, 491, 595, 709, 833, 967, 1111, 1265, 1429, 1603, 1787, 1981, 2185, 2399, 2623, 2857, 3101, 3355, 3619, 3893, 4177, 4471, 4775, 5089, 5413, 5747, 6091, 6445, 6809, 7183, 7567, 7961, 8365, 8779, 9203, 9637, 10081, 10535
OFFSET
0,2
FORMULA
From Vincenzo Librandi, Jul 06 2012: (Start)
G.f.: (1+2*x+7*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
a(n) = 2*A005476(n) + 1. - Bruno Berselli, Jul 06 2012
E.g.f.: exp(x)*(1 + 4*x + 5*x^2). - Elmo R. Oliveira, Oct 31 2024
MATHEMATICA
CoefficientList[Series[(7*x^2+2*x+1)/(1-x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Jul 06 2012 *)
Table[5n^2-n+1, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 5, 19}, 50] (* Harvey P. Dale, Aug 06 2022 *)
PROG
(Magma) [ 5*n^2-n+1: n in [0..50] ];
(PARI) a(n)=5*n^2-n+1 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A005476.
Sequence in context: A022267 A094465 A020580 * A146616 A146395 A154302
KEYWORD
nonn,easy,changed
AUTHOR
Vincenzo Librandi, Jan 29 2010
EXTENSIONS
Replaced definition with formula. - N. J. A. Sloane, Mar 03 2010
STATUS
approved