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 A160182 Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix. 2
 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 5, 2, 1, 1, 1, 6, 2, 1, 1, 1, 1, 10, 4, 2, 1, 1, 1, 1, 11, 4, 2, 1, 1, 1, 1, 1, 16, 6, 3, 2, 1, 1, 1, 1, 1, 19, 7, 4, 2, 1, 1, 1, 1, 1, 1, 26, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Inverse mobius transform (A051731) * the triangle shifts row terms to the right deleting the right border, getting triangle A160183: (1; 2,1; 3,1,1; 5,2,1,1;...). LINKS Table of n, a(n) for n=1..66. FORMULA Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix. The operations shift the inverse Mobius transform (A051731) down, changing the signs to (-1), then add I = (1,1,1,...) as the right border. EXAMPLE First few rows of the triangle: 1; 1, 1; 2, 1, 1; 3, 1, 1, 1; 5, 2, 1, 1, 1; 6, 2, 1, 1, 1, 1; 10, 4, 2, 1, 1, 1, 1; 11, 4, 2, 1, 1, 1, 1, 1; 16, 6, 3, 2, 1, 1, 1, 1, 1; 19, 7, 4, 2, 1, 1, 1, 1, 1, 1; 26, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1; ... MAPLE A160182den := proc(n, k) a := add( A129184(n, i)*A051731(i, k), i=1..n) ; if n =k then -a+1 ; else -a; end if; end proc: N := 20 : M := Matrix(N, N) : for n from 1 to N do for k from 1 to N do M[n, k] := A160182den(n, k) ; end do: end do: MatrixInverse(M) ; # R. J. Mathar, Aug 04 2015 CROSSREFS Cf. A051731, A129184, A160183. Row sums = A068336. Left border = A003238. Sequence in context: A124021 A109626 A182285 * A195825 A098824 A181651 Adjacent sequences: A160179 A160180 A160181 * A160183 A160184 A160185 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, May 03 2009 STATUS approved

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Last modified April 16 05:35 EDT 2024. Contains 371697 sequences. (Running on oeis4.)