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A008417
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Crystal ball sequence for 8-dimensional cubic lattice.
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4
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1, 17, 145, 833, 3649, 13073, 40081, 108545, 265729, 598417, 1256465, 2485825, 4673345, 8405905, 14546705, 24331777, 39490049, 62390545, 96220561, 145198913, 214828609, 312193553, 446304145, 628496897, 872893441, 1196924561, 1621925137, 2173806145, 2883810113, 3789356689, 4934985233
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OFFSET
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0,2
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COMMENTS
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This is row/column 8 of the Delannoy numbers array, A008288, which is the main entry for these numbers, listing many more properties. - Shel Kaphan, Jan 06 2023
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LINKS
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J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
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FORMULA
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G.f.: (1+x)^8/(1-x)^9.
a(n) = (2*n^8 + 8*n^7 + 84*n^6 + 224*n^5 + 798*n^4 + 1232*n^3 + 1636*n^2 + 1056*n + 315)/315. - Alexander Adamchuk, May 23 2006
Sum_{n >= 1} (-1)^(n+1)/(n*a(n-1)*a(n)) = log(2) - (1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 + 1/7 - 1/8). - Peter Bala, Mar 23 2024
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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