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A027689
a(n) = n^2 + n + 4.
11
4, 6, 10, 16, 24, 34, 46, 60, 76, 94, 114, 136, 160, 186, 214, 244, 276, 310, 346, 384, 424, 466, 510, 556, 604, 654, 706, 760, 816, 874, 934, 996, 1060, 1126, 1194, 1264, 1336, 1410, 1486, 1564, 1644, 1726, 1810, 1896, 1984, 2074, 2166, 2260, 2356, 2454, 2554
OFFSET
0,1
FORMULA
a(n) = A000217(n-2) + A000217(n+2) for n > 0. - Jon Perry, Jul 23 2003
a(n) = 2*n + a(n-1)-2 (with a(1)=4). - Vincenzo Librandi, Aug 05 2010
Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(15)/2)/sqrt(15). - Amiram Eldar, Jan 18 2021
From Elmo R. Oliveira, Oct 28 2024: (Start)
G.f.: 2*(2 - 3*x + 2*x^2)/(1 - x)^3.
E.g.f.: (2*(2 + x) + x^2)*exp(x).
a(n) = 2*A152948(n+2). (End)
MAPLE
with (combinat):seq(fibonacci(3, n)+n+3, n=0..47); # Zerinvary Lajos, Jun 07 2008
MATHEMATICA
Table[n^2+n+4, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011 *)
LinearRecurrence[{3, -3, 1}, {4, 6, 10}, 50] (* or *) CoefficientList[ Series[ (-4+6*x-4*x^2)/(-1+x)^3, {x, 0, 50}], x] (* Harvey P. Dale, Dec 18 2021 *)
PROG
(PARI) a(n)=n^2+n+4 \\ Charles R Greathouse IV, Oct 07 2015
(GAP) List([0..50], n->n^2+n+4); # Muniru A Asiru, Jul 15 2018
CROSSREFS
KEYWORD
nonn,easy,changed
STATUS
approved