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A001849 Crystal ball sequence for 7-dimensional cubic lattice.
(Formerly M4979 N2139)
8
1, 15, 113, 575, 2241, 7183, 19825, 48639, 108545, 224143, 433905, 795455, 1392065, 2340495, 3800305, 5984767, 9173505, 13726991, 20103025, 28875327, 40754369, 56610575, 77500017, 104692735, 139703809, 184327311, 240673265, 311207743, 398796225, 506750351 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 81.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. G. Stanton and D. D. Cowan, Note on a "square" functional equation, SIAM Rev., 12 (1970), 277-279.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for crystal ball sequences

FORMULA

G.f.: (1+x)^7 /(1-x)^8.

a(n) = (8*n^7+28*n^6+224*n^5+490*n^4+1232*n^3+1372*n^2+1056*n+315)/315 - Johannes W. Meijer, Jul 14 2013

MAPLE

A001849:=(z+1)**7/(z-1)**8; [Conjectured by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

CoefficientList[Series[(z + 1)^7/(z - 1)^8, {z, 0, 200}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)

CROSSREFS

Cf. A001848, A001849.

Cf. A240876.

Sequence in context: A295384 A110822 A222410 * A115150 A115138 A233326

Adjacent sequences:  A001846 A001847 A001848 * A001850 A001851 A001852

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 24 18:55 EST 2021. Contains 341584 sequences. (Running on oeis4.)