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A027690 a(n) = n^2 + n + 5. 10
5, 7, 11, 17, 25, 35, 47, 61, 77, 95, 115, 137, 161, 187, 215, 245, 277, 311, 347, 385, 425, 467, 511, 557, 605, 655, 707, 761, 817, 875, 935, 997, 1061, 1127, 1195, 1265, 1337, 1411, 1487, 1565, 1645, 1727, 1811, 1897, 1985, 2075, 2167, 2261 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..47.

Patrick De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X)

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = A176271(n + 1, 3) for n > 1. - Reinhard Zumkeller, Apr 13 2010

a(n) = 2*n + a(n-1) for n>0, a(0)=5. - Vincenzo Librandi, Aug 05 2010

From Ilya Gutkovskiy, Nov 25 2016: (Start)

G.f.: (5 - 8*x + 5*x^2)/(1 - x)^3.

Sum_{n>=0} 1/a(n) = Pi*tanh(sqrt(19)*Pi/2)/sqrt(19) = 0.720729156259... (End)

MAPLE

with (combinat):seq(fibonacci(3, n)+n+4, n=0..47); # Zerinvary Lajos, Jun 07 2008

MATHEMATICA

Table[n^2 + n + 5, {n, 0, 100}] (* T. D. Noe, Oct 29 2009 *)

PROG

(PARI) a(n)=n^2+n+5 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A002061, A002522.

Sequence in context: A067830 A191019 A106862 * A087200 A153118 A145987

Adjacent sequences:  A027687 A027688 A027689 * A027691 A027692 A027693

KEYWORD

nonn,easy

AUTHOR

Patrick De Geest

EXTENSIONS

Corrected by T. D. Noe, Nov 09 2006

Definition and offset fixed by Franklin T. Adams-Watters, Jul 06 2009

STATUS

approved

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Last modified May 6 12:27 EDT 2021. Contains 343585 sequences. (Running on oeis4.)