A022264 a(n) = n*(7*n - 1)/2.

0, 3, 13, 30, 54, 85, 123, 168, 220, 279, 345, 418, 498, 585, 679, 780, 888, 1003, 1125, 1254, 1390, 1533, 1683, 1840, 2004, 2175, 2353, 2538, 2730, 2929, 3135, 3348, 3568, 3795, 4029, 4270, 4518, 4773, 5035, 5304, 5580, 5863, 6153, 6450, 6754, 7065, 7383

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 13, ..., and the parallel line from 3, in the direction 3, 30, ..., in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. - Omar E. Pol, Sep 09 2011

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Leo Tavares, Illustration: Crysta-gons

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

Formula

a(n) = C(7*n,2)/7, n >= 0. - Zerinvary Lajos, Jan 02 2007

a(n) = A049450(n) + A000217(n). - Reinhard Zumkeller, Oct 09 2008

a(n) = 7*n + a(n-1) - 4 for n > 0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

a(n) = (2*n)^2 - n*(n+1)/2 = A016742(n) - A000217(n). - Philippe Deléham, Mar 08 2013

a(n) = A174738(7*n+2). - Philippe Deléham, Mar 26 2013

G.f.: x*(3 + 4*x)/(1 - x)^3. - R. J. Mathar, Aug 04 2016

a(n) = A000217(4*n-1) - A000217(3*n-1). - Bruno Berselli, Oct 17 2016

a(n) = (1/5) * Sum_{i=n..(6*n-1)} i. - Wesley Ivan Hurt, Dec 04 2016

E.g.f.: (1/2)*x*(7*x + 6)*exp(x). - G. C. Greubel, Aug 19 2017

a(n) = A005449(n) + A000384(n). See Crysta-gons illustration. - Leo Tavares, Nov 21 2021

Maple

[seq(binomial(7*n, 2)/7, n=0..37)]; # Zerinvary Lajos, Jan 02 2007

Mathematica

Table[n (7*n - 1)/2, {n, 0, 40}] (* Zerinvary Lajos, Jul 10 2009 *)

Prog

(PARI) a(n)=n*(7*n-1)/2 \\ Charles R Greathouse IV, Mar 08 2013
(Magma) [n*(7*n-1)/2 : n in [0..50]]; // Wesley Ivan Hurt, Dec 04 2016

Crossrefs

Cf. A000217, A022265.

Cf. sequences listed in A254963.

Cf. similar sequences listed in A022288.

Cf. A016742, A049450, A174738, A195019, A195020.

Cf. A005449, A000384.

Sequence in context: A051805 A352267 A330451 * A288541 A296014 A273337

Adjacent sequences: A022261 A022262 A022263 * A022265 A022266 A022267

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved