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.

A002916 High temperature series for spin-1/2 Ising specific heat on 3-dimensional simple cubic lattice.

Original entry on oeis.org

3, 33, 564, 8976, 155124, 2791308, 51382068, 962178084, 18258531348, 350143322088, 6772382631732, 131922552534036, 2585198190891636, 50919899448451512, 1007393565758096820, 20007153991627682124, 398699967207692643924, 7969220499183448073760, 159718349893920279061428
Offset: 0

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Author

Keywords

References

  • S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Equals 3*A001408.
Cf. A002917 (b.c.c.), A002918 (f.c.c.), A001393 (partition function), A010571 (internal energy), A002913 (susceptibility), A002169 (Heisenberg model), A029872 (square, low-temperature).

Programs

Formula

Sum_{n>=0} a(n) * v^(2*n) = (v^2-1) * (-q/2*f(v)^2 - (v^2-1) * f'(v)^2 + f(v) * (2*v*f'(v) + (v^2-1)*f''(v))) / f(v)^2, where f(v) = Sum_{n>=0} A001393(n) * v^(2*n) and q = 6 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 15 2022

Extensions

Corrections and updates from Steven Finch
Terms a(13) and beyond from Andrey Zabolotskiy, Feb 15 2022