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A204243 Determinant of the n-th principal submatrix of A204242. 3
1, 2, 11, 144, 4149, 251622, 31340799, 7913773980, 4024015413705, 4106387069191890, 8395359475529822355, 34357677843892688699400, 281336437060919094044274525, 4608419756389534634440592965950, 150992374805715685629827976712244775 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..80

Wikipedia, Matrix determinant lemma

FORMULA

a(n) = (1 - Sum_{k=2..n} 1/(2^k-1)) * Product_{k=2..n} (2^k-1) = 2*A005329(n) - A203011(n). - Robert Israel, Nov 30 2015

MAPLE

f:= n -> (1 - add(1/(2^i-1), i=2..n))*mul(2^i-1, i=2..n):

seq(f(n), n=1..30); # 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 *)

PROG

(PARI) vector(20, n, matdet(matrix(n, n, i, j, if(i==1, 1, if(j==1, 1, if(i==j, 2^i-1)))))) \\ Colin Barker, Nov 27 2015

CROSSREFS

Cf. A005329, A203011, A204238, A204242.

Sequence in context: A113148 A193209 A268743 * A203203 A046912 A185245

Adjacent sequences:  A204240 A204241 A204242 * A204244 A204245 A204246

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 13 2012

STATUS

approved

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Last modified July 26 01:13 EDT 2021. Contains 346294 sequences. (Running on oeis4.)