A008414 Coordination sequence for 6-dimensional cubic lattice.
1, 12, 72, 292, 912, 2364, 5336, 10836, 20256, 35436, 58728, 93060, 142000, 209820, 301560, 423092, 581184, 783564, 1038984, 1357284, 1749456, 2227708, 2805528, 3497748, 4320608, 5291820, 6430632, 7757892, 9296112, 11069532
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
- J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
- Milan Janjic, Two Enumerative Functions
- Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.
- Ross McPhedran, Numerical Investigations of the Keiper-Li Criterion for the Riemann Hypothesis, arXiv:2311.06294 [math.NT], 2023. See p. 6.
- Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).
Programs
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Maple
for n from 1 to 8 do eval(4*n*(2/15*n^4+4/3*n^2+23/15)) od;
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Mathematica
{1}~Join~Table[4 n (2/15 n^4 + 4/3 n^2 + 23/15), {n, 29}] (* or *) CoefficientList[Series[((1 + x)/(1 - x))^6, {x, 0, 29}], x] (* Michael De Vlieger, Oct 04 2016 *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,12,72,292,912,2364,5336},30] (* Harvey P. Dale, Jul 01 2020 *) -
PARI
a(n)=if(n, 4*n*(2*n^4+20*n^2+23)/15, 1) \\ Charles R Greathouse IV, Oct 04 2016
Formula
G.f.: ((1+x)/(1-x))^6.
a(n) = 4*n*(2/15*n^4+4/3*n^2+23/15) for n > 0. - S. Bujnowski (slawb(AT)atr.bydgoszcz.pl), Nov 26 2002
n*a(n) = 12*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018
Comments