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 A117165 Triangle of coefficients for the Shift-Moebius transform, read by rows. 10
 1, -1, 1, -2, 0, 1, -1, -1, 0, 1, -2, -1, 0, 0, 1, 1, -2, -1, 0, 0, 1, -1, -1, -1, 0, 0, 0, 1, 3, -2, -1, -1, 0, 0, 0, 1, 0, 0, -2, -1, 0, 0, 0, 0, 1, 4, -2, -1, -1, -1, 0, 0, 0, 0, 1, 4, 0, -2, -1, -1, 0, 0, 0, 0, 0, 1, 5, 1, -1, -2, -1, -1, 0, 0, 0, 0, 0, 1, 1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 7, 0, 0, -2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Column k = Shift-Moebius transform of a sequence of all zeros except for a single '1' in position k: [0,0,0,..(k-1)zeros..,1,0,0,0,...]. Column 1 is A117166, the Shift-Moebius transform of [1,0,0,0,...]. Column 2 is A117167, the Shift-Moebius transform of [0,1,0,0,...]. Column 3 is A117168, the Shift-Moebius transform of [0,0,1,0,...]. Row sums give A117169, the Shift-Moebius transform of [1,1,1,...]. LINKS FORMULA The Shift-Moebius transform of a sequence B is equal to the limit of the iteration: let C_1 = B and for k>1, C_{k+1} = Moebius transform of C_k preceded by k zeros, then shift left k places (to drop the leading k zeros). Triangle A117162 is a good example, starting with A008683 in column 1 as C_1 and each column k, C_k, is obtained using the above iteration, so that the columns converge to A117166. EXAMPLE Triangle begins: 1; -1, 1; -2, 0, 1; -1,-1, 0, 1; -2,-1, 0, 0, 1; 1,-2,-1, 0, 0, 1; -1,-1,-1, 0, 0, 0, 1; 3,-2,-1,-1, 0, 0, 0, 1; 0, 0,-2,-1, 0, 0, 0, 0, 1; 4,-2,-1,-1,-1, 0, 0, 0, 0, 1; 4, 0,-2,-1,-1, 0, 0, 0, 0, 0, 1; 5, 1,-1,-2,-1,-1, 0, 0, 0, 0, 0, 1; 1, 2,-1,-1,-1,-1, 0, 0, 0, 0, 0, 0, 1; 7, 0, 0,-2,-1,-1,-1, 0, 0, 0, 0, 0, 0, 1; 6, 3,-2,-1,-2,-1,-1, 0, 0, 0, 0, 0, 0, 0, 1; 5, 3, 1,-2,-1,-1,-1,-1, 0, 0, 0, 0, 0, 0, 0, 1; ... PROG (PARI) {T(n, k)=if(n=c, if((r+n-i)%(c+n-i)==0, moebius((r+n-i)/(c+n-i)), 0))))[ n, k])} CROSSREFS Cf. A117166 (column 1), A117167 (column 2), A117168 (column 3), A117169 (row sums), A117170 (inverse), A117162, A008683; A117175. Sequence in context: A074272 A105553 A262696 * A213629 A278522 A024363 Adjacent sequences:  A117162 A117163 A117164 * A117166 A117167 A117168 KEYWORD sign,tabl AUTHOR Wouter Meeussen and Paul D. Hanna, Mar 05 2006 STATUS approved

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