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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000217, A022265.

Cf. sequences listed in A254963.

Cf. similar sequences listed in A022288.

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

Cf. A005449, A000384.

Programs

Magma

[n*(7*n-1)/2 : n in [0..50]]; // Wesley Ivan Hurt, Dec 04 2016

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 *)

PARI

a(n)=n*(7*n-1)/2 \\ Charles R Greathouse IV, Mar 08 2013

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