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Search: id:A078125
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| A078125 |
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First column of matrix A078123, which is the square of the infinite lower triangular matrix A078122 that shifts left and up when cubed. |
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+0
16
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| 1, 2, 5, 23, 239, 5828, 342383, 50110484, 18757984046, 18318289003448, 47398244089264547, 329030840161393127681, 6190927493941741957366100, 318447442589056401640929570896, 45106654667152833836835578059359839
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = sum of the n-th row of lower triangular matrix of A078122. Conjecture: a(n) = the partitions of 3^n into powers of 3.
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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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MATHEMATICA
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m[i_, j_] := m[i, j]=If[j==0||i==j, 1, m3[i-1, j-1]]; m2[i_, j_] := m2[i, j]=Sum[m[i, k]m[k, j], {k, j, i}]; m3[i_, j_] := m3[i, j]=Sum[m[i, k]m2[k, j], {k, j, i}]; a[n_] := m2[n, 0]
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CROSSREFS
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Cf. A078121, A078122 (matrix shift when cubed), A078123, A078124.
Adjacent sequences: A078122 A078123 A078124 this_sequence A078126 A078127 A078128
Sequence in context: A032182 A136731 A062495 this_sequence A034692 A002507 A137094
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 18 2002
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