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 A261357 Pyramid of coefficients in expansion of (1 + 2*x + 2*y)^n. 3
 1, 1, 2, 2, 1, 4, 4, 4, 8, 4, 1, 6, 6, 12, 24, 12, 8, 24, 24, 8, 1, 8, 8, 24, 48, 24, 32, 96, 96, 32, 16, 64, 96, 64, 16, 1, 10, 10, 40, 80, 40, 80, 240, 240, 80, 80, 320, 480, 320, 80, 32, 160, 320, 320, 160, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS T(n,j,k) is the number of lattice paths from (0,0,0) to (n,j,k) with steps (1,0,0), two kinds of steps (1,1,0) and two kinds of steps (1,1,1). The sum of the numbers in each slice of the pyramid is 5^n. The terms of the j-th row of the n-th slice of this pyramid are the sum of the terms in each antidiagonal of the j-th triangle of the n-th slice of A261358. - Dimitri Boscainos, Aug 21 2015 LINKS Alois P. Heinz, Rows n = 0..38, flattened FORMULA T(i+1,j,k) = 2*T(i,j-1,k-1)+ 2*T(i,j-1,k) + T(i,j,k); T(i,j,-1) = 0, ...; T(0,0,0) = 1. T(n,j,k) = 2^j*binomial(n,j)*binomial(j,k). - Dimitri Boscainos, Aug 21 2015 EXAMPLE Here is the fourth (n=3) slice of the pyramid:         1       6   6    12  24  12   8  24  24   8 MAPLE p:= proc(i, j, k) option remember;       if k<0 or i<0 or i>k or j<0 or j>i then 0     elif {i, j, k}={0} then 1     else p(i, j, k-1) +2*p(i-1, j, k-1) +2*p(i-1, j-1, k-1)       fi     end: seq(seq(seq(p(i, j, k), j=0..i), i=0..k), k=0..5); # Adapted from Alois P. Heinz's Maple program for A261356 PROG (PARI) tabf(nn) = {for (n=0, nn, for (j=0, n, for (k=0, j, print1(2^j*binomial(n, j)*binomial(j, k), ", ")); print(); ); print(); ); } \\ Michel Marcus, Oct 07 2015 CROSSREFS Cf. A046816, A261356, A261358. Sequence in context: A136787 A165038 A305191 * A238870 A213946 A145036 Adjacent sequences:  A261354 A261355 A261356 * A261358 A261359 A261360 KEYWORD nonn,tabf,walk AUTHOR Dimitri Boscainos, Aug 16 2015 STATUS approved

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Last modified January 22 19:16 EST 2020. Contains 331153 sequences. (Running on oeis4.)