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Search: id:A109283
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| 1, 1, 3, 15, 96, 735, 6447, 63120, 677739, 7878921, 98216466, 1302951903, 18283530882, 270031107630, 4180037999178, 67581115214649, 1137710941143720, 19890998444408631, 360327514948457178, 6749464344626557092
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OFFSET
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0,3
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COMMENT
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Triangular matrix T=A109282 satisfies: T(n,k) = [T^3](n-1,k) for n>k+1>=1, with T(n,n) = 1 and T(n+1,n) = n+1 for n>=0; also, T^(m+3) = SHIFT_UP(T^(m+1) - T^m) - D*T^m for all m where diagonal matrix D = [0,1,2,3,...] and SHIFT_UP shifts each column up 1 row.
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PROGRAM
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(PARI) {a(n)=local(M=matrix(n+1, n+1)); M=M^0; for(i=1, n, M=matrix(n+1, n+1, r, c, if(r>=c, if(r==c, 1, if(r==c+1, c, (M^3)[r-1, c]))))); return(M[n+1, 1])}
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CROSSREFS
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Cf. A109153, A109282 (triangle), A109284 (column 1), A109285 (column 2), A109286 (row sums).
Sequence in context: A128240 A076301 A112913 this_sequence A079689 A108442 A060148
Adjacent sequences: A109280 A109281 A109282 this_sequence A109284 A109285 A109286
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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), Jun 24 2005
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