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A033582
a(n) = 7*n^2.
15
0, 7, 28, 63, 112, 175, 252, 343, 448, 567, 700, 847, 1008, 1183, 1372, 1575, 1792, 2023, 2268, 2527, 2800, 3087, 3388, 3703, 4032, 4375, 4732, 5103, 5488, 5887, 6300, 6727, 7168, 7623, 8092, 8575, 9072, 9583, 10108, 10647, 11200, 11767, 12348, 12943, 13552, 14175
OFFSET
0,2
COMMENTS
From Roberto E. Martinez II, Jan 07 2002: (Start)
Number of edges of the complete bipartite graph of order 8n, K_n,7n.
Number of edges of the complete tripartite graph of order 5n, K_n,n,3n. (End)
FORMULA
Central terms of the triangle in A132111: a(n) = A132111(2*n,n). - Reinhard Zumkeller, Aug 10 2007
a(n) = 7*A000290(n). - Omar E. Pol, Dec 11 2008
a(n) = 14*n + a(n-1) - 7 (with a(0) = 0). - Vincenzo Librandi, Aug 05 2010
G.f.: -7*x*(1+x)/(x-1)^3. - R. J. Mathar, Feb 06 2017
From Amiram Eldar, Feb 03 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/42.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/84.
Product_{n>=1} (1 + 1/a(n)) = sqrt(7)*sinh(Pi/sqrt(7))/Pi.
Product_{n>=1} (1 - 1/a(n)) = sqrt(7)*sin(Pi/sqrt(7))/Pi. (End)
From Elmo R. Oliveira, Dec 02 2024: (Start)
E.g.f.: 7*exp(x)*x*(1 + x).
a(n) = n*A008589(n) = A195041(2*n).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MATHEMATICA
7Range[0, 49]^2 (* Alonso del Arte, Jun 30 2013 *)
PROG
(PARI) a(n)=7*n^2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved