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A008415 Coordination sequence for 7-dimensional cubic lattice. 5
1, 14, 98, 462, 1666, 4942, 12642, 28814, 59906, 115598, 209762, 361550, 596610, 948430, 1459810, 2184462, 3188738, 4553486, 6376034, 8772302, 11879042, 15856206, 20889442, 27192718, 35011074, 44623502, 56345954, 70534478 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.

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

FORMULA

G.f.: ((1+x)/(1-x))^7.

a(n) = 4*n*n*(2*n*n + 7)*(n*n + 14)/45 + 2 - 0^n. - George F. Johnson, Feb 21 2013

a(n) = A008414(n) + A008414(n-1) + a(n-1). - Bruce J. Nicholson, Dec 17 2017

n*a(n) = 14*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018

MATHEMATICA

CoefficientList[Series[((1+x)/(1-x))^7, {x, 0, 30}], x] (* Harvey P. Dale, Oct 11 2015 *)

PROG

(Python) # replace leading dots with blanks

R=[]

for n in range(29):

....r=4*n*n*(2*n*n +7)*(n*n +14)/45 +2-0**n

....R=R+[r]

print R

# George F. Johnson Feb 02 2013

(PARI) a(n) = 2*(4*n^6+70*n^4+196*n^2+45)/45-0^n; \\ Altug Alkan, Dec 18 2017

CROSSREFS

Cf. A008414.

Sequence in context: A254469 A296987 A008534 * A003206 A206257 A101376

Adjacent sequences:  A008412 A008413 A008414 * A008416 A008417 A008418

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)