A064762 a(n) = 21*n^2.

0, 21, 84, 189, 336, 525, 756, 1029, 1344, 1701, 2100, 2541, 3024, 3549, 4116, 4725, 5376, 6069, 6804, 7581, 8400, 9261, 10164, 11109, 12096, 13125, 14196, 15309, 16464, 17661, 18900, 20181, 21504, 22869, 24276, 25725, 27216, 28749

Offset: 0

Author

Roberto E. Martinez II, Oct 18 2001

Keywords

• nonn
• easy

Comments

Number of edges in a complete 7-partite graph of order 7n, K_n,n,n,n,n,n,n.

Links

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

Crossrefs

Similar sequences are listed in A244630.

Cf. A000217, A000290, A033428, A033581, A033582, A033583.

Cf. A008603, A195049.

Programs

Magma

[21*n^2 : n in [0..50]]; // Wesley Ivan Hurt, Jul 04 2014

Mathematica

21 Range[0, 50]^2 (* Wesley Ivan Hurt, Jul 04 2014 *)
LinearRecurrence[{3,-3,1},{0,21,84},40] (* Harvey P. Dale, Jul 29 2019 *)

PARI

a(n)=21*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 42*n + a(n-1) - 21 for n > 0, a(0)=0. - Vincenzo Librandi, Aug 07 2010

a(n) = 21*A000290(n) = 7*A033428(n) = 3*A033582(n). - Omar E. Pol, Jul 03 2014

a(n) = t(7*n) - 7*t(n), where t(i) = i*(i+k)/2 for any k. Special case (k=1): a(n) = A000217(7*n) - 7*A000217(n). - Bruno Berselli, Aug 31 2017

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

G.f.: 21*x*(1 + x)/(1-x)^3.

E.g.f.: 21*x*(1 + x)*exp(x).

a(n) = n*A008603(n) = A195049(2*n).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)