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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))]]:=

    <seq(2^(k+1)-1, 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.)