A187710 a(n) = n^2 + n + 10.

10, 12, 16, 22, 30, 40, 52, 66, 82, 100, 120, 142, 166, 192, 220, 250, 282, 316, 352, 390, 430, 472, 516, 562, 610, 660, 712, 766, 822, 880, 940, 1002, 1066, 1132, 1200, 1270, 1342, 1416, 1492, 1570, 1650, 1732, 1816, 1902, 1990, 2080, 2172, 2266, 2362, 2460

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

a(0)=10, a(1)=12, a(2)=16; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jan 18 2014

From Bruno Berselli, Oct 20 2016: (Start)

G.f.: 2*(5 - 9*x + 5*x^2)/(1 - x)^3.

a(n) = 2*A167499(n-1) for n>0.

a(n) = Sum_{i=n-5..n+5} i*(i+1)/11. (End)

E.g.f.: (x^2 + 2*x + 10)*exp(x). - G. C. Greubel, Nov 06 2018

Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(39)/2)/sqrt(39). - Amiram Eldar, Jan 17 2021

Mathematica

f[n_] := n^2 + n + 10; f[Range[0, 100]]
LinearRecurrence[{3, -3, 1}, {10, 12, 16}, 50] (* Harvey P. Dale, Jan 18 2014 *)

Prog

(PARI) a(n)=n^2+n+10 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [n^2 + n + 10: n in [0..50]]; // G. C. Greubel, Nov 06 2018

Crossrefs

Cf. A002061, A002378, A167499.

Sequence in context: A334939 A063192 A109604 * A063096 A270819 A031183

Adjacent sequences: A187707 A187708 A187709 * A187711 A187712 A187713

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Mar 12 2011

Extensions

Offset changed to 0 from Bruno Berselli, Oct 20 2016

Status

approved