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

%I A045900 #18 Jul 05 2025 08:09:06
%S A045900 1,1,3,8,25,85,318,1234,4884,19458,77727,310761,1242853,4971151,
%T A045900 19884270,79536639,318145993,1272583241,5090332042,20361326983,
%U A045900 81445306447,325781223902,1303124893253,5212499570050,20849998276525,83399993101506,333599972400353
%N A045900 Hypothetical numbers of terms in general expressions for coefficients of Lovelock Lagrangians.
%C A045900 Hypothetical extension of sequence A006372.
%H A045900 Vaclav Kotesovec, <a href="/A045900/b045900.txt">Table of n, a(n) for n = 0..1000</a>
%H A045900 C. C. Briggs, <a href="http://arXiv.org/abs/gr-qc/9607033">A General Expression for the Quintic Lovelock Tensor</a>, arXiv:gr-qc/9607033, 1996-1997.
%H A045900 C. C. Briggs, <a href="http://arXiv.org/abs/gr-qc/9703074">A General Expression for the Quartic Lovelock Tensor</a>, arXiv:gr-qc/9703074, 1997.
%H A045900 C. C. Briggs, <a href="http://arXiv.org/abs/gr-qc/9808050">Some Possible Features of General Expressions for Lovelock Tensors ...</a>, arXiv:gr-qc/9808050, 1998-2000.
%F A045900 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.
%F A045900 a(n) ~ 2^(2*n+1) / 27. - _Vaclav Kotesovec_, Jul 05 2025
%t A045900 p = PartitionsP;
%t A045900 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)];
%t A045900 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Feb 24 2019 *)
%Y A045900 Cf. A000041, A006372.
%K A045900 nonn
%O A045900 0,3
%A A045900 C. C. Briggs (ccb104(AT)psu.edu)
%E A045900 More terms from _Jean-François Alcover_, Feb 24 2019