A016826 -id:A016826 - cp's OEIS frontend

A016830 a(n) = (4*n+2)^6.

64, 46656, 1000000, 7529536, 34012224, 113379904, 308915776, 729000000, 1544804416, 3010936384, 5489031744, 9474296896, 15625000000, 24794911296, 38068692544, 56800235584, 82653950016, 117649000000, 164206490176, 225199600704, 304006671424, 404567235136, 531441000000

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A016758, A016825, A016826, A016827.

(4*Range[0,20]+2)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{64,46656,1000000,7529536,34012224,113379904,308915776},20] (* Harvey P. Dale, Oct 14 2012 *)

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Harvey P. Dale, Oct 14 2012
From Amiram Eldar, Jul 07 2022: (Start)
a(n) = A016825(n)^6 = A016826(n)^3 = A016827(n)^2 = 64*A016758(n).
Sum_{n>=0} 1/a(n) = Pi^6/61440. (End)

A199833 Number of -n..n arrays of 4 elements with zero sum and no two neighbors summing to zero.

Original entry on oeis.org

4, 40, 140, 336, 660, 1144, 1820, 2720, 3876, 5320, 7084, 9200, 11700, 14616, 17980, 21824, 26180, 31080, 36556, 42640, 49364, 56760, 64860, 73696, 83300, 93704, 104940, 117040, 130036, 143960, 158844, 174720, 191620, 209576, 228620, 248784

Offset: 1

R. H. Hardin, Nov 11 2011

nonn

			Some solutions for n=3:
   0  -3  -3   0   0   0  -1   1   1  -1   0   0  -3  -2  -1  -2
  -2   2  -1   3   1   1   0   1  -2   2  -2   1   2   1  -3   0
   3   3   2   0   2   1  -1  -3   1   0   0   0  -1  -2   1   1
  -1  -2   2  -3  -3  -2   2   1   0  -1   2  -1   2   3   3   1

R. H. Hardin, Table of n, a(n) for n = 1..200

Row 2 of A199832.

Cf. A000447, A016826.

Empirical: a(n) = (16/3)*n^3 - (4/3)*n = 4*A000447(n).
Empirical: G.f.: 4*x*(1+6*x+x^2) / (x-1)^4 . - R. J. Mathar, Aug 01 2014
Empirical: partial sums of A016826. - Sean A. Irvine, Jul 13 2022

cp's OEIS Frontend

A016830 a(n) = (4*n+2)^6.

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