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A022264 a(n) = n*(7*n - 1)/2. 21
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 (list; graph; refs; listen; history; text; internal format)
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

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) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2, a(0)=0, a(1)=3 and a(2)=13. - Paolo P. Lava, Jul 29 2009

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

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.

Sequence in context: A183436 A154300 A051805 * A288541 A296014 A273337

Adjacent sequences:  A022261 A022262 A022263 * A022265 A022266 A022267

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 21 04:43 EST 2018. Contains 299389 sequences. (Running on oeis4.)