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 A261360 Pentatope of coefficients in expansion of (1 + 2*x + 2*y + 2*z)^n. 2
 1, 1, 2, 2, 2, 1, 4, 4, 4, 4, 8, 8, 4, 8, 4, 1, 6, 6, 6, 12, 24, 24, 12, 24, 12, 8, 24, 24, 24, 48, 24, 8, 24, 24, 8, 1, 8, 8, 8, 24, 48, 48, 24, 48, 24, 32, 96, 96, 96, 192, 96, 32, 96, 96, 32, 16, 64, 64, 96, 192, 96, 64, 192, 192, 64, 16, 64, 96, 64, 96, 1, 10, 10, 10, 40, 80, 80, 40, 80, 40, 80, 240, 240, 240, 480, 240, 80, 240, 240, 80, 80, 320, 320, 480, 960, 480, 320, 960, 960, 320, 80, 320, 480, 320, 80, 32, 160, 160, 320, 640, 320, 320, 960, 960, 320, 160, 640, 960, 640, 160, 32, 160, 320, 320, 160, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS T(n,i,j,k) is the number of lattice paths from (0,0,0,0) to (n,i,j,k) with steps (1,0,0,0) and two kinds of steps (1,1,0,0), (1,1,1,0) and (1,1,1,1). The sum of the numbers in each cell of the pentatope is 7^n (A000420). LINKS FORMULA T(i+1,j,k,l) = 2*T(i,j-1,k-1,l-1) + 2*T(i,j-1,k-1,l) + 2*T(i,j-1,k,l) + T(i,j,k,l); T(i,j,k,-1)=0, ...; T(0,0,0,0)=1. T(n,i,j,k) = 2^i*binomial(n,i)*binomial(i,j)*binomial(j,k). - Dimitri Boscainos, Aug 21 2015 EXAMPLE The 5th slice (n=4) of this 4D simplex starts at a(35). It comprises a 3D tetrahedron of 35 terms whose sum is 2401. It is organized as follows: . .               1 . .               8 .            8     8 . .              24 .           48    48 .        24    48    24 . .              32 .           96    96 .        96   192    96 .     32    96    96    32 . .              16 .           64    64 .        96   192    96 .     64   192   192    64 .  16    64    96    64    16 MAPLE p:= proc(i, j, k, l) option remember;       if l<0 or j<0 or i<0 or i>l or j>i or k<0 or k>j then 0     elif {i, j, k, l}={0} then 1     else p(i, j, k, l-1) +2*p(i-1, j, k, l-1) +2*p(i-1, j-1, k, l-1)+2*p(i-1, j-1, k-1, l-1)       fi     end: seq(seq(seq(seq(p(i, j, k, l), k=0..j), j=0..i), i=0..l), l=0..5); # Adapted from Alois P. Heinz's Maple program for A261356 PROG (PARI) lista(nn) = {for (n=0, nn, for (i=0, n, for (j=0, i, for (k=0, j, print1(2^i*binomial(n, i)*binomial(i, j)*binomial(j, k), ", ")); ); ); ); } \\ Michel Marcus, Oct 07 2015 CROSSREFS Cf. A000420, A189225, A261358, A261359. Sequence in context: A071458 A247719 A131308 * A184242 A307739 A109978 Adjacent sequences:  A261357 A261358 A261359 * A261361 A261362 A261363 KEYWORD nonn,tabf,walk,less AUTHOR Dimitri Boscainos, Aug 16 2015 STATUS approved

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)