The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A229955 Triangular array read by rows: 3 dimensional analog of A227997. 0
 8, 152, 64, 5056, 2432, 512, 205720, 104000, 29184, 4096, 9305152, 4828544, 1525248, 311296, 32768, 449404224, 236984448, 79898624, 19226624, 3112960, 262144, 22695553536, 12099474432, 4251479040, 1123909632, 221839360, 29884416, 2097152, 1183891745688, 636162156096, 230017430016, 64636047360, 14330265600, 2413559808, 278921216, 16777216 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS T(n,k) is the number of walks on the 3 dimensional grid that start and end at the origin using 2n steps and having exactly k primitive loops. The steps are in the eight directions: (1,1,1), (1,1,-1), (1,-1,1), (1,-1,-1), (-1,1,1), (-1,1,-1), (-1,-1,1), (-1,-1,-1).  A primitive loop is a walk that starts and ends on the origin but does not otherwise touch the origin. Column 1 is A094059. Row sums are A002897. LINKS FORMULA G.f.: 1/( 1 - y*(1 - 1/A(x)) ) where A(x) is the o.g.f. for A002897. Generally for such walks in N dimensions:  1/( 1 - y*(1 - 1/B(x)) ) where B(x) = Sum_{n>=0} binomial(2n,n)^N*x^n. EXAMPLE 8, 152, 64, 5056, 2432, 512, 205720, 104000, 29184, 4096, 9305152, 4828544, 1525248, 311296, 32768, 449404224, 236984448, 79898624, 19226624, 3112960, 262144 MATHEMATICA nn=6; a=Sum[Binomial[2n, n]^3x^n, {n, 0, nn}]; Map[Select[#, #>0&]&, Drop[CoefficientList[Series[1/(1-y(1-1/a)), {x, 0, nn}], {x, y}], 1]]//Grid CROSSREFS Sequence in context: A264642 A300872 A217502 * A249481 A003491 A053606 Adjacent sequences:  A229952 A229953 A229954 * A229956 A229957 A229958 KEYWORD nonn,tabl,walk AUTHOR Geoffrey Critzer, Oct 04 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 23 13:56 EST 2020. Contains 331171 sequences. (Running on oeis4.)