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 A115361 Inverse of matrix (1,x)-(x,x^2) (expressed in Riordan array notation). 23
 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are the 'ruler function' A001511. Columns are stretched Fredholm-Rueppel sequences (A036987). Inverse is A115359. Eigensequence of triangle A115361 = A018819 starting with offset 1: (1, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 20, 20, ...). - Gary W. Adamson, Nov 21 2009 From Gary W. Adamson, Nov 27 2009: (Start) A115361 * [1, 2, 3, ...] = A129527 = (1, 3, 3, 7, 5, 9, 7, 15, ...). (A115361)^(-1) * [1, 2, 3, ...] = A115359 * [1, 2, 3, ...] = A026741 starting /Q (1, 1, 3, 2, 5, 3, 7, 4, 9, ...). (End) This is the lower-left triangular part of the inverse of the infinite matrix A_{ij} = [i=j] - [i=2j], its upper-right part (above / right to the diagonal) being zero. The n-th row has 1 in column n/2^i, i = 0, 1, ... as long as this is an integer. - M. F. Hasler, May 13 2018 LINKS FORMULA Number triangle whose k-th column has g.f. x^k*sum{j>=0} x^((2^j-1)*(k+1)). T(n,k) = A209229((n+1)/(k+1)) for k+1 divides n+1, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 05 2018 EXAMPLE Triangle begins: 1; 1,1; 0,0,1; 1,1,0,1; 0,0,0,0,1; 0,0,1,0,0,1; 0,0,0,0,0,0,1; 1,1,0,1,0,0,0,1; 0,0,0,0,0,0,0,0,1; 0,0,0,0,1,0,0,0,0,1; 0,0,0,0,0,0,0,0,0,0,1; MAPLE A115361 := proc(n, k)     for j from 0 do         if k+(2*j-1)*(k+1) > n then             return 0 ;         elif k+(2^j-1)*(k+1) = n then             return 1 ;         end if;     end do; end proc: # R. J. Mathar, Jul 14 2012 MATHEMATICA (*recurrence*) Clear[t] t[1, 1] = 1; t[n_, k_] := t[n, k] =   If[k == 1, Sum[t[n, k + i], {i, 1, 2 - 1}],    If[Mod[n, k] == 0, t[n/k, 1], 0], 0] Flatten[Table[Table[t[n, k], {k, 1, n}], {n, 14}]] (* Mats Granvik, Jun 26 2014 *) PROG (PARI) tabl(nn) = {T = matrix(nn, nn, n, k, n--; k--; if ((n==k), 1, if (n==2*k+1, -1, 0))); Ti = T^(-1); for (n=1, nn, for (k=1, n, print1(Ti[n, k], ", "); ); print(); ); } \\ Michel Marcus, Mar 28 2015 (PARI) A115361_row(n, v=vector(n))={until(bittest(n, 0)||!n\=2, v[n]=1); v} \\ Yields the n-th row (of length n). - M. F. Hasler, May 13 2018 (PARI) T(n, k)={if(n%k, 0, my(e=valuation(n/k, 2)); n/k==1<

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)