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A078123
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Square of infinite lower triangular matrix A078122.
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4
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1, 2, 1, 5, 6, 1, 23, 51, 18, 1, 239, 861, 477, 54, 1, 5828, 32856, 25263, 4347, 162, 1, 342383, 3013980, 3016107, 699813, 39285, 486, 1, 50110484, 690729981, 865184724, 253656252, 19053063, 354051, 1458, 1, 18757984046, 406279238154
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Rows n = 0..60, flattened
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FORMULA
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M(1, j) = A078125(j), M(j+1, j)=2*3^j.
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EXAMPLE
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Square of A078122 = A078123 as can be seen by 4 X 4 submatrix:
[1,_0,_0,0]^2=[_1,_0,_0,_0]
[1,_1,_0,0]___[_2,_1,_0,_0]
[1,_3,_1,0]___[_5,_6,_1,_0]
[1,12,_9,1]___[23,51,18,_1]
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MAPLE
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S:= proc(i, j) option remember;
add(M(i, k)*M(k, j), k=0..i)
end:
M:= proc(i, j) option remember; `if`(j=0 or i=j, 1,
add(S(i-1, k)*M(k, j-1), k=0..i-1))
end:
seq(seq(S(n, k), k=0..n), n=0..10); # Alois P. Heinz, Feb 27 2015
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MATHEMATICA
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S[i_, j_] := S[i, j] = Sum[M[i, k]*M[k, j], {k, 0, i}]; M[i_, j_] := M[i, j] = If[j == 0 || i == j, 1, Sum[S[i-1, k]*M[k, j-1], {k, 0, i-1}]]; Table[Table[S[n, k], {k, 0, n}], {n, 0, 10}] // Flatten (* Jean-François Alcover, Mar 06 2015, after Alois P. Heinz *)
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CROSSREFS
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Cf. A078121, A078122, A078124, A078125.
Sequence in context: A178121 A302595 A113345 * A323312 A231774 A209170
Adjacent sequences: A078120 A078121 A078122 * A078124 A078125 A078126
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna, Nov 18 2002
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STATUS
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approved
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