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Search: id:A109286
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| 1, 2, 6, 25, 146, 1074, 9247, 89618, 956106, 11066959, 137531624, 1820347008, 25499542444, 376098118280, 5815744322556, 93946244699173, 1580463050838884, 27616009578136506, 500029604169802336, 9362566904514285044
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OFFSET
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0,2
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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(sum(k=0, n, M[n+1, k+1]))}
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CROSSREFS
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Cf. A109155, A109282 (triangle), A109283 (column 0), A109284 (column 1), A109285 (column 2).
Sequence in context: A084784 A135881 A007815 this_sequence A009466 A032479 A029988
Adjacent sequences: A109283 A109284 A109285 this_sequence A109287 A109288 A109289
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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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