A045900 Hypothetical numbers of terms in general expressions for coefficients of Lovelock Lagrangians.

1, 1, 3, 8, 25, 85, 318, 1234, 4884, 19458, 77727, 310761, 1242853, 4971151, 19884270, 79536639, 318145993, 1272583241, 5090332042, 20361326983, 81445306447, 325781223902, 1303124893253, 5212499570050, 20849998276525, 83399993101506, 333599972400353

Offset

0,3

Comments

Hypothetical extension of sequence A006372.

Links

Table of n, a(n) for n=0..26.

C. C. Briggs, A General Expression for the Quintic Lovelock Tensor, arXiv:gr-qc/9607033, 1996-1997.

C. C. Briggs, A General Expression for the Quartic Lovelock Tensor, arXiv:gr-qc/9703074, 1997.

C. C. Briggs, Some Possible Features of General Expressions for Lovelock Tensors ..., arXiv:gr-qc/9808050, 1998-2000.

Formula

a(n+3) = 3*a(n+2) - 3*a(n+1) + a(n) + p(n+3) - 3*p(n+2) + 3*p(n+1) - p(n) + 2^(2*n + 1); a(n+4) = 7*a(n+3) - 15*a(n+2) + 13*a(n+1) - 4*a(n) + p(n+4) - 7*p(n+3) + 15*p(n+2) - 13*p(n+1) + 4*p(n); where p(n) is the partition function (i.e. number of partitions of n, A000041) and where p(0) = 1.

Mathematica

p = PartitionsP;
a[n_] := a[n] = If[n < 4, {1, 1, 3, 8}[[n+1]], a[n-3] - 3*a[n-2] + 3*a[n-1] - p[n-3] + 3*p[n-2] - 3*p[n-1] + p[n] + 2^(2*(n-3) + 1)];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 24 2019 *)

Crossrefs

Cf. A000041, A006372.

Sequence in context: A038665 A172382 A151426 * A000738 A006372 A148798

Adjacent sequences: A045897 A045898 A045899 * A045901 A045902 A045903

Keyword

nonn

Author

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

Extensions

More terms from Jean-François Alcover, Feb 24 2019

Status

approved