A100040 a(n) = 2*n^2 + n - 5.

-5, -2, 5, 16, 31, 50, 73, 100, 131, 166, 205, 248, 295, 346, 401, 460, 523, 590, 661, 736, 815, 898, 985, 1076, 1171, 1270, 1373, 1480, 1591, 1706, 1825, 1948, 2075, 2206, 2341, 2480, 2623, 2770, 2921, 3076, 3235, 3398, 3565, 3736, 3911, 4090, 4273

Offset: 0

Author

Reinhard Zumkeller, Oct 31 2004

Keywords

• sign
• easy

Comments

a(n) is the result of taking five consecutive numbers starting at n-2, then adding the products of the first and the last and of the second with the fourth and finally adding the middle term. That is, a(n) = (n^2-4) + (n^2-1) + n. - J. M. Bergot, Mar 06 2018

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).

Crossrefs

Cf. A100036, A100037, A100038, A100039.

Programs

GAP

List([0..50],n->2*n^2+n-5); # Muniru A Asiru, Mar 20 2018

Magma

[ 2*n^2+n-5: n in [0..50] ];

Maple

[seq(2*n^2+n-5,n=0..50)]; # Muniru A Asiru, Mar 20 2018

Mathematica

Table[2*n^2 + n - 5, {n, 0, 50}] (* G. C. Greubel, Jul 15 2017 *)
LinearRecurrence[{3,-3,1},{-5,-2,5},50] (* Harvey P. Dale, Sep 21 2017 *)

PARI

a(n)=2*n^2+n-5 \\ Charles R Greathouse IV, Sep 24 2015

Formula

A100035(a(n)) = 4 for n>3;

a(n) = A014105(n) - 5 = A084849(n) - 6 = A100041(n) + 2.

a(n) = 2*a(n-1)-a(n-2)+4; a(0)=-5, a(1)=-2. - Vincenzo Librandi, Dec 26 2010

G.f.: (-5 + 13*x - 4*x^2)/(1 - x)^3. - Arkadiusz Wesolowski, Dec 25 2011

E.g.f.: (2*x^2 + 3*x - 5)*exp(x). - G. C. Greubel, Jul 15 2017