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.

Showing 1-3 of 3 results.

A006372 Numbers of terms in expressions for coefficients of "Lovelock Lagrangians" (or "Gauss-Bonnet forms") in terms of Riemann-Christoffel curvature tensor and two of its contractions (viz., the Ricci curvature tensor and the Riemann curvature scalar) for n-dimensional differentiable manifolds having a general linear connection.

Original entry on oeis.org

1, 1, 3, 8, 25, 85, 397, 2183, 15129, 122585
Offset: 0

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Author

C. C. Briggs (ccb104(AT)vm.cac.psu.edu)

Keywords

Crossrefs

Cf. A006373, A045900 (conjectural), A306892 (2-regular digraphs).

Extensions

a(6)-a(8) from R. J. Mathar, Apr 08 2019
a(9) added by R. J. Mathar, Apr 15 2019

A167551 The row sums of the ED1 array A167546 read by antidiagonals.

Original entry on oeis.org

1, 2, 7, 26, 115, 596, 3623, 25462, 203939, 1836032, 18361831, 201984098, 2423820227, 31509694204, 441135811847, 6617037458606, 105872600222083, 1799834206605272, 32397015728269319, 615543298868687962
Offset: 1

Views

Author

Johannes W. Meijer, Nov 10 2009

Keywords

Comments

The first six terms coincide with the known first six terms of A006373.

Crossrefs

Cf. A006373.
A167546 is the ED1 array.

A030429 a(n+2) = 7*a(n+1) - 7*a(n) - 9*n; a(n+4) = 9*a(n+3) - 22*a(n+2) + 21*a(n+1) - 7*a(n).

Original entry on oeis.org

1, 2, 7, 26, 115, 596, 3331, 19100, 110329, 638540, 3697405, 21411974, 124001893, 718129334, 4158891979, 24085338398, 139485124807, 807798504728, 4678193659303, 27092766081872, 156902006957821
Offset: 0

Views

Author

Keywords

Comments

Hypothetical numbers of terms in general expressions for Lovelock tensors. Hypothetical extension of sequence A006373 - C. C. Briggs (ccb104(AT)psu.edu)

Crossrefs

Cf. A006373.

Programs

  • Mathematica
    LinearRecurrence[{9,-22,21,-7},{1,2,7,26},30] (* Harvey P. Dale, Oct 12 2015 *)

Formula

Expansion of (1-7*x+11*x^2-14*x^3)/((1-7*x+7*x^2)*(x-1)^2).
a(n) = 2*(23*A030240(n)-133*A030240(n-1)) -9*n -45. - R. J. Mathar, Mar 14 2011
Showing 1-3 of 3 results.