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A027688
a(n) = n^2 + n + 3.
18
3, 5, 9, 15, 23, 33, 45, 59, 75, 93, 113, 135, 159, 185, 213, 243, 275, 309, 345, 383, 423, 465, 509, 555, 603, 653, 705, 759, 815, 873, 933, 995, 1059, 1125, 1193, 1263, 1335, 1409, 1485, 1563, 1643, 1725, 1809, 1895, 1983, 2073, 2165, 2259, 2355, 2453, 2553, 2655
OFFSET
0,1
FORMULA
For n > 0: a(n) = A176271(n+1,2). - Reinhard Zumkeller, Apr 13 2010
a(n) = 2*n + a(n-1) (with a(0)=3). - Vincenzo Librandi, Aug 05 2010
From Colin Barker, Dec 29 2014: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (3*x^2 - 4*x + 3)/(1 - x)^3. (End)
Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(11)/2)/sqrt(11). - Amiram Eldar, Jan 17 2021
E.g.f.: exp(x)*(3 + 2*x + x^2). - Elmo R. Oliveira, Oct 31 2024
MAPLE
with (combinat):seq(fibonacci(3, n)+n+2, n=0..47); # Zerinvary Lajos, Jun 07 2008
MATHEMATICA
Table[n^2 + n + 3, {n, 0, 50}] (* Bruno Berselli, Sep 03 2018 *)
PROG
(PARI) Vec((3*x^2-4*x+3)/(1-x)^3 + O(x^100)) \\ Colin Barker, Dec 29 2014
CROSSREFS
Sequence in context: A022940 A025207 A118403 * A033498 A147493 A178961
KEYWORD
nonn,easy
EXTENSIONS
Definition and offset corrected by Franklin T. Adams-Watters, Jul 06 2009
STATUS
approved

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