A195322 a(n) = 20*n^2.

0, 20, 80, 180, 320, 500, 720, 980, 1280, 1620, 2000, 2420, 2880, 3380, 3920, 4500, 5120, 5780, 6480, 7220, 8000, 8820, 9680, 10580, 11520, 12500, 13520, 14580, 15680, 16820, 18000, 19220, 20480, 21780, 23120, 24500, 25920, 27380, 28880, 30420, 32000, 33620, 35280

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 20, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Semiaxis opposite to A195317 in the same spiral.

a(n) is the sum of all the integers less than 10*n which are not multiple of 2 or 5. a(2) = (1 + 3 + 7 + 9) + (11 + 13 + 17 + 19) = 20 + 60 = 80 = 20 * 2^2. (Link Crux Mathematicorum). - Bernard Schott, May 15 2017

Number of terms less than 10^k (k=0, 1, 2, ...): 1, 1, 3, 8, 23, 71, 224, 708, 2237, 7072, 22361, 70711, ... - Muniru A Asiru, Feb 01 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Léo Sauvé, Problem 53, Crux Mathematicorum, Vol. 1, Nov. 1975, page 88.

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

Formula

a(n) = 20*A000290(n) = 10*A001105(n) = 5*A016742(n) = 4*A033429(n) = 2*A033583(n).

a(0)=0, a(1)=20, a(2)=80; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jan 18 2013

a(n) = A010014(n) - A005899(n) for n > 0. - R. J. Cano, Sep 29 2015

From Elmo R. Oliveira, Nov 30 2024: (Start)

G.f.: 20*x*(1 + x)/(1-x)^3.

E.g.f.: 20*x*(1 + x)*exp(x).

a(n) = n*A008602(n) = A195148(2*n). (End)

Example

From Muniru A Asiru, Feb 01 2018: (Start)
n=0, a(0) = 20*0^2 = 0.
n=1, a(1) = 20*1^2 = 20.
n=1, a(2) = 20*2^2 = 80.
n=1, a(3) = 20*3^2 = 180.
n=1, a(4) = 20*4^2 = 320.
...
(End)

Maple

a := n -> 20*n^2; seq(a(n), n=0..10^3); # Muniru A Asiru, Feb 01 2018

Mathematica

20 Range[0, 40]^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 20, 80}, 50] (* Harvey P. Dale, Jan 18 2013 *)

Prog

(Magma) [20*n^2: n in [0..40]]; // Vincenzo Librandi, Sep 20 2011
(PARI) a(n) = 20*n^2 \\ Charles R Greathouse IV, Oct 07 2015
(GAP) List([0..10^3], n->20*n^2); # Muniru A Asiru, Feb 01 2018

Crossrefs

Bisection of A195148.

Cf. A016802, A033581, A033583, A135453, A139098, A144555, A195321, A195323.

Cf. A000290, A001105, A005899, A010014, A016742, A033429, A195162, A195317.

Cf. A008602.

Sequence in context: A292360 A337988 A002609 * A200424 A211463 A244449

Adjacent sequences: A195319 A195320 A195321 * A195323 A195324 A195325

Keyword

nonn,easy

Author

Omar E. Pol, Sep 16 2011

Status

approved