A119493 -id:A119493 - cp's OEIS frontend

A119508 Determinant of n X n matrix of first n^2 terms of Euler totient function phi (A000010).

1, 0, -16, 80, -4640, -1696, -47290368, 778240, -1252408320, 827269120, -1883587535170560, -167527809024, -660985839681085440, -66300178824585216, -1744375183677849600, 29157688117836220727296, 5544673967679230591621398528, -134078707495836661579776

Offset: 1

Jonathan Vos Post, May 27 2006

			a(2) = 0 because of the singular matrix 0 =
|1 1|
|2 2|.

Harvey P. Dale, Table of n, a(n) for n = 1..250

Cf. A000010, A119493.

nmax = 20; Table[Det[Table[EulerPhi[k*(i-1) + j], {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* Vaclav Kotesovec, Feb 24 2019 *)
Table[Det[Partition[EulerPhi[Range[n^2]],n]],{n,20}] (* Harvey P. Dale, Jul 28 2021 *)

More terms from Vaclav Kotesovec, Feb 24 2019

A119514 Determinant of n X n matrix of first n^2 squarefree numbers.

Original entry on oeis.org

1, -1, -4, -84, 64, 320, 1540, -4296, 22774, -11504, -5472, 13752, -18325, -4808916, 22766346, 5005440, 519618712, -216839949, -913585532, 4352326994, 15724880927, 0, -44298224496, 783852776697, -173267864064, -601092343023697, 26866456767483, 39073758546015

Offset: 1

Jonathan Vos Post, May 27 2006

The absolute value of a(1) through a(3) and a(5), are squares. None of the absolute values of a(1) through a(8) are themselves squarefree.

			a(2) = -1 =
|1 2|
|3 5|.
a(3) = -4 =
|.1..2..3|
|.5..6..7|
|10.11.13|.

Amiram Eldar, Table of n, a(n) for n = 1..898

Cf. A005117, A119493.

s = Select[Range[1500], SquareFreeQ]; n = Length[s]; m = Floor[Sqrt[n]]; seq = {}; Do[mat = Partition[s[[1 ;; k^2]], k]; AppendTo[seq, Det[mat]], {k, 1, m}]; seq (* Amiram Eldar, Aug 23 2019 *)
Module[{nn=30,sqfr},sqfr=Select[Range[2 nn^2],SquareFreeQ];Table[Det[ Partition[ Take[ sqfr,n^2],n]],{n,nn}]] (* Harvey P. Dale, Jul 09 2022 *)

More terms from Amiram Eldar, Aug 23 2019

A119528 Determinant of n X n matrix of first n^2 number of trees with n unlabeled nodes (A000055).

Original entry on oeis.org

1, 0, 7, -7288, 210319661226, -28724163065553504725184, -17273218743083166095017987886925095168489136, -3262865955763797132157936566332771517266609360571691111615623236765760

Offset: 1

Jonathan Vos Post, May 27 2006

			a(3) = 7 =
|.1..1..1|
|.1..2..3|
|.6.11.23|.

Alois P. Heinz, Table of n, a(n) for n = 1..17

Cf. A000055, A119493.

More terms from Alois P. Heinz, Sep 26 2011

A119510 Determinant of n X n matrix of first n^2 terms of prime powers A000961.

Original entry on oeis.org

1, -2, 4, -18, 6, 1638, -592, 446088, 39036424, -284293536, -1842401824, 248900267136, -15845288960, -7495661063424, 759742256093184, -10356544812377088, -3243279301721283584, 12699358712830242816, 4118558014200840683520, -64593095335200293474304, -1944280313362776777097216

Offset: 1

Jonathan Vos Post, May 27 2006

			a(2) = -2 = |1 2|
            |3 4|.
a(3) = 4 = |1 2 3|
           |4 5 7|
           |8 9 11|.

Cf. A000015, A000961, A119493.

More terms from Hugo Pfoertner, Sep 13 2024

A119512 Determinant of n X n matrix of first n^2 terms of A000020 number of primitive polynomials of degree n over GF(2).

Original entry on oeis.org

2, 2, 244, -80544, 2895473496576

Offset: 1

Jonathan Vos Post, May 27 2006

The initial 2 should probably be a 1, see: A011260. This would change all terms to: a(2) = 0 because of the singular determinant[1,1,2,2] = 0; a(3) = 52; a(4) = -34848; a(5) = -2211008492544.

			a(2) = 2 =
|2 1|
|2 2|.

Cf. A000020, A011260, A119493.

A119522 Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers.

Original entry on oeis.org

1, -8, -27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Jonathan Vos Post, May 27 2006

			a(3) = -27 =
|.1..3..6|
|10.15.21|
|28.36.45|.
a(4) = 0 because of the singular matrix 0 =
|.1...3...6..10|
|15..21..28..36|
|45..55..66..78|
|91.105.120.136|.

Cf. A000217, A119493.

nmax = 100; Table[Det[Table[(k*(i-1) + j)*(k*(i-1) + j + 1)/2, {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* Vaclav Kotesovec, Feb 24 2019 *)

a(n) = determinant of n X n matrix of first n^2 nonzero terms of A000217(k) for k>0. a(n) = determinant of n X n matrix of k*(k+1)/2 for k from 1 through n^2.

More terms from Vaclav Kotesovec, Feb 24 2019

A119525 Determinant of n X n matrix of first n^2 nonzero terms of A000332 binomial coefficients binomial(n,4).

Original entry on oeis.org

1, -40, -8505, 9765625, 0

Offset: 1

Jonathan Vos Post, May 27 2006

a(5) = 5^10.

			a(3) = -8505 =
|..1...5..15|
|.35..70.126|
|210.330.495|.
a(4) = 0 because of the singular matrix 0 =
|.1...3...6..10|
|15..21..28..36|
|45..55..66..78|
|91.105.120.136|.

Cf. A000217, A119493.

A119527 Determinant of n X n matrix of first n^2 partition numbers (A000041).

Original entry on oeis.org

1, 1, -4, 40, -17570, 29277, 1612051490, -98797189506, 24519692392546611, -1102715711997300050, -4167252029989605007510429722, -29479989614260596083347544, 4174157347638693670019191622559426971168, 139672908285735171626083209102943170111074

Offset: 1

Jonathan Vos Post, May 27 2006

			a(3) = -4 =
|.1..1..2|
|.3..5..7|
|11.15.22|.

Cf. A000041, A119493.

nmax = 15; Table[Det[Table[PartitionsP[k*(i-1) + j-1], {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* Vaclav Kotesovec, Feb 24 2019 *)

More terms from Vaclav Kotesovec, Feb 24 2019

A119530 Determinant of n X n matrix of first n^2 odious numbers: odd number of 1's in binary expansion (A000069).

Original entry on oeis.org

1, -1, 12, 0, -409, 0, 4144, 0, 5040, 0, 142291, 0, 29139, 0, 0, 0, 0, 0, -71577990, 0, 3815616, 0, -288128476, 0, -248768000, 0, 0, 0, -28714176, 0, 0, 0, 0, 0, -6040500480, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -795328048345114368

Offset: 1

Jonathan Vos Post, May 27 2006

sign

			a(3) = 12 =
  | 1  2  4|
  | 7  8 11|
  |13 14 16|.
a(4) = 0 because of the singular matrix 0 =
  | 1  2  4  7|
  | 8 11 13 14|
  |16 19 21 22|
  |25 26 28 31|.
a(6) = 0 because of the singular matrix whose lower right entry is 127.

Cf. A000069, A119493.

nn=10000;With[{xa=Select[Range[nn],OddQ[DigitCount[#,2,1]]&]},Table[Det[ Partition[Take[xa,n^2],n]],{n,Floor[Sqrt[Length[xa]]]}]] (* Harvey P. Dale, Jun 28 2012 *)

a(n)=matdet(matrix(n,n,i,j,k=(i-1)*n+j;2*k-1-hammingweight(k-1)%2)) \\ Charles R Greathouse IV, Mar 29 2013

More terms from Harvey P. Dale, Jun 28 2012

A119537 Determinant of n X n matrices of first n^2 denumerants (A000115).

Original entry on oeis.org

1, 0, -3, -3, 0, -54, 343, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Jonathan Vos Post, May 28 2006

Conjecture: a(n>7)=0. - Robert G. Wilson v, Jun 07 2006

			a(6) = -54 = -2 * 3^3. a(7) = 343 = 7^3.
a(8) = 0 because of the singular matrix 0 =
|..1...1...2...2...3...4...5...6|
|..7...8..10..11..13..14..16..18|
|.20..22..24..26..29..31..34..36|
|.39..42..45..48..51..54..58..61|
|.65..68..72..76..80..84..88..92|
|.97.101.106.110.115.120.125.130|
|135.140.146.151.157.162.168.174|
|180.186.192.198.205.211.218.224|.

Cf. A000115, A119493.

clst = CoefficientList[ Series[1/((1 - x)(1 - x^2)(1 - x^5)), {x, 0, 105^2 - 1}], x];
f[n_] := Det[ Partition[ Take[clst, n^2], n]];
Array[f,100] (* Robert G. Wilson v, Jun 07 2006 *)

a(n) = determinant[A000115(k) from k=1 to n^2].

More terms from Robert G. Wilson v, Jun 07 2006

cp's OEIS Frontend

A119508 Determinant of n X n matrix of first n^2 terms of Euler totient function phi (A000010).

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A119514 Determinant of n X n matrix of first n^2 squarefree numbers.

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A119528 Determinant of n X n matrix of first n^2 number of trees with n unlabeled nodes (A000055).

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A119510 Determinant of n X n matrix of first n^2 terms of prime powers A000961.

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A119512 Determinant of n X n matrix of first n^2 terms of A000020 number of primitive polynomials of degree n over GF(2).

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A119522 Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers.

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A119525 Determinant of n X n matrix of first n^2 nonzero terms of A000332 binomial coefficients binomial(n,4).

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A119527 Determinant of n X n matrix of first n^2 partition numbers (A000041).

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A119530 Determinant of n X n matrix of first n^2 odious numbers: odd number of 1's in binary expansion (A000069).

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