cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-25 of 25 results.

A158045 Determinant of power series with alternate signs of gamma matrix with determinant 2!.

Original entry on oeis.org

2, 0, 26, 0, 502, 0, 10306, 0, 213902, 0, 4448666, 0, 92558182, 0, 1925894386, 0, 40073418302, 0, 833837682506, 0, 17350295562262, 0, 361020847688866, 0, 7512036585662702, 0, 156308684773943546, 0, 3252434233373292742, 0, 67675884159595889746, 0
Offset: 1

Views

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Keywords

Comments

a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n), where A is the submatrix A(1..3,1..3) of the matrix with factorial determinant
A = [[1,1,1,1,1,1,...], [1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]. Note: Determinant A(1..n,1..n) = (n-1)!.

Examples

			a(1) = Determinant(A) = 2! = 2.

References

  • G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.

Crossrefs

Cf. A111490, A158040-A158044.

Programs

  • Maple
    seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)), n=1..30);
  • PARI
    vector(100, n, matdet(sum(k=1, n, [1,1,1 ; 1,2,1 ; 1,2,3]^k*(-1)^(k-1)))) \\ Colin Barker, Jul 13 2014

Formula

Empirical g.f.: -2*x*(2*x^2 -1)*(4*x^4 -11*x^2 +1) / ((x -1)*(x +1)*(2*x -1)*(2*x +1)*(2*x^2 -5*x +1)*(2*x^2 +5*x +1)). - Colin Barker, Jul 13 2014

Extensions

More terms, and offset changed to 1 by Colin Barker, Jul 13 2014

A158046 Determinant of power series with alternate signs of gamma matrix with determinant 3!.

Original entry on oeis.org

6, -12, 294, -4800, 33006, -868476, 8045022, -133497600, 1840843662, -23069939772, 357884304366, -4506695659200, 65700186820638, -892588899692796, 12240418932523614, -172125321194572800, 2335747604463776238, -32681605781959208508, 448728077274231515214
Offset: 1

Views

Author

Giorgio Balzarotti and Paolo P. Lava, Mar 11 2009

Keywords

Comments

a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n).
where A is the submatrix A(1..4,1..4) of the matrix with factorial determinant
A = [[1,1,1,1,1,1,...], [1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]; note: Determinant A(1..n,1..n) = (n-1)!.
a(n) is even with respect to signs of power of A.

Examples

			a(1) = Determinant(A) = 3! = 6.

References

  • G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008

Crossrefs

Cf. A111490, A158040-A158045.

Programs

  • Maple
    with(LinearAlgebra):
A:= Matrix([[1, 1, 1, 1], [1, 2, 1, 2], [1, 2, 3, 1], [1, 2, 3, 4]]):
a:= n-> Determinant(add(A^i*(-1)^(i-1), i=1..n)):
seq(a(n), n=1..30);
  • PARI
    vector(100, n, matdet(sum(k=1, n, [1,1,1,1 ; 1,2,1,2 ; 1,2,3,1 ; 1,2,3,4]^k*(-1)^(k-1)))) \\ Colin Barker, Jul 14 2014

Formula

Empirical g.f.: -6*x*(6*x^2 -1)*(46656*x^12 -190512*x^10 +60480*x^9 +243432*x^8 -21168*x^7 -100984*x^6 -3528*x^5 +6762*x^4 +280*x^3 -147*x^2 +1) / ((x -1)*(6*x -1)*(6*x^4 +22*x^3 +23*x^2 +10*x +1)*(216*x^4 +360*x^3 +138*x^2 +22*x +1)*(216*x^6 -828*x^5 +1284*x^4 -808*x^3 +214*x^2 -23*x +1)). - Colin Barker, Jul 14 2014

Extensions

More terms, and offset changed to 1 by Colin Barker, Jul 14 2014

A158047 Determinant of power series with alternate signs of gamma matrix with determinant 4!.

Original entry on oeis.org

24, 144, 13896, 842400, 36604920, 2333944368, 126441557448, 6680853691200, 387982670513688, 20676854461594320, 1158249535425969384, 63778918790403180000, 3507499386329443453752, 194248225087593045241968
Offset: 0

Views

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Keywords

Comments

a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n)
where A is the submatrix A(1..5,1..5) of the matrix with factorial determinant
A = [[1,1,1,1,1,1,...], [1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]; note: Determinant A(1..n,1..n) = (n-1)!.

Examples

			a(1) = Determinant(A) = 4! = 24.

References

  • G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.

Crossrefs

Cf. A111490, A158040-A158046.

Programs

  • Maple
    seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)),n=1..30);

A158048 Determinant of power series with alternate signs of gamma matrix with determinant 5!.

Original entry on oeis.org

120, -3120, 1657560, -462870720, 94034430600, -34709926327440, 7736751469771080, -2418878906762872320, 634745166256592831640, -175970074271706846159600, 49274372699370917797432920
Offset: 0

Views

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Keywords

Comments

a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n)
where A is the submatrix A(1..6,1..6) of the matrix with factorial determinant
A = [[1,1,1,1,1,1,...], [1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]; note: Determinant A(1..n,1..n) = (n-1)!.
a(n) is even with respect to signs of power of A.

Examples

			a(1) = Determinant(A) = 5! = 120.

References

  • G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.

Crossrefs

Cf. A111490, A158040-A158047.

Programs

  • Maple
    seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)),n=1..30);

A158049 Determinant of power series with alternate signs of gamma matrix with determinant 6!.

Original entry on oeis.org

720, 95760, 323885520, 520091041680, 646101191031120, 1426723480107570960, 1908953197598354801040, 3574028285578402656777360, 5645446200753726958758372240, 9359837643523957747903959388560
Offset: 0

Views

Author

Giorgio Balzarotti & Paolo P. Lava, Mar 11 2009

Keywords

Comments

a(n) = Determinant(A - A^2 + A^3 - A^4 + A^5 - ... - (-1)^n*A^n)
where A is the submatrix A(1..7,1..7) of the matrix with factorial determinant
A = [[1,1,1,1,1,1,...], [1,2,1,2,1,2,...], [1,2,3,1,2,3,...], [1,2,3,4,1,2,...], [1,2,3,4,5,1,...], [1,2,3,4,5,6,...], ...]; note: Determinant A(1..n,1..n) = (n-1)!.

Examples

			a(1) = Determinant(A) = 6! = 720.

References

  • G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008.

Crossrefs

Cf. A111490, A158040-A158048.

Programs

  • Maple
    seq(Determinant(sum(A^i*(-1)^(i-1),i=1..n)),n=1..30);
Previous Showing 21-25 of 25 results.

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