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 A204242 Infinite symmetric matrix given by f(i,1)=1, f(1,j)=1, f(i,i)=2^i-1 and f(i,j)=0 otherwise, read by antidiagonals. 2
 1, 1, 1, 1, 3, 1, 1, 0, 0, 1, 1, 0, 7, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 15, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 31, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 63, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA From Robert Israel, Nov 30 2015: (Start) a(k*(k+1)/2) = a(1 + k*(k+1)/2) = 1. a(2*k^2 + 2*k + 1) = 2^(k+1) - 1. a(n) = 0 otherwise. (End) EXAMPLE Northwest corner: 1 1 1 1 1 3 0 0 1 0 7 0 1 0 0 15 MAPLE N:= 1000: # to get a(1) to a(N) V:= Vector(N): V[[seq(k*(k+1)/2, k= 1..floor((sqrt(8*N+1)-1)/2))]]:= 1: V[[seq(1+k*(k+1)/2, k=1..floor((sqrt(8*N-7)-1)/2))]]:= 1: V[[seq(1+2*k+2*k^2, k=0..floor((sqrt(2*N-1)-1)/2))]]:=     : convert(V, list); # Robert Israel, Nov 30 2015 MATHEMATICA f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1; f[i_, i_] := 2^i - 1; m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[8]] (* 8x8 principal submatrix *) Flatten[Table[f[i, n + 1 - i],   {n, 1, 12}, {i, 1, n}]]     (* A204242 *) Table[Det[m[n]], {n, 1, 15}]  (* A204243 *) Permanent[m_] :=   With[{a = Array[x, Length[m]]},    Coefficient[Times @@ (m.a), Times @@ a]]; Table[Permanent[m[n]], {n, 1, 15}]   (* A203011 *) CROSSREFS Cf. A204243, A203011. Sequence in context: A339632 A115718 A204181 * A211313 A321609 A238414 Adjacent sequences:  A204239 A204240 A204241 * A204243 A204244 A204245 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 13 2012 EXTENSIONS Name edited by Robert Israel, Nov 30 2015 STATUS approved

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Last modified May 12 10:54 EDT 2021. Contains 343821 sequences. (Running on oeis4.)