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.

A046918 Triangle of coefficients of polynomials p(n), with p(3)=1, p(n) = (1 - t^(2*n - 4))*(1 - t^(2*n - 3))*p(n - 1)/((1 - t^(n - 3))*(1 - t^n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 2, 2, 1, 1, 1, 1, 2, 3, 4, 5, 7, 7, 8, 8, 8, 7, 7, 5, 4, 3, 2, 1, 1, 1, 1, 2, 3, 5, 6, 9, 11, 14, 16, 19, 20, 23, 23, 24, 23, 23, 20, 19, 16, 14, 11, 9, 6, 5, 3, 2, 1, 1, 1, 1, 2, 3, 5, 7, 10, 13, 18, 22, 28, 33, 40, 45, 52, 57, 63, 66, 70, 71
Offset: 3

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Examples

			1;
1 + t + t^2 + t^3 + t^4 + t^5;
t^10 + t^9 + 2*t^8 + 2*t^7 + 3*t^6 + 3*t^5 + 3*t^4 + 2*t^3 + 2*t^2 + t + 1;
...
		

Crossrefs

Cf. A046919.

Programs

  • Maple
    p := proc(n) option remember; if n = 3 then 1 else (1-t^(2*n-4))*(1-t^(2*n-3))*p(n-1)/((1-t^(n-3))*(1-t^n)); fi; end;
  • Mathematica
    p[3] = 1; p[n_] := p[n] = (1 - t^(2*n-4))*(1 - t^(2*n-3))*p[n-1]/((1 - t^(n-3))*(1 - t^n)) // Simplify; Table[ CoefficientList[ Series[p[n], {t, 0, n^3}], t], {n, 3, 8}] // Flatten (* Jean-François Alcover, Oct 25 2013 *)

Extensions

Keyword tabf by Michel Marcus, Dec 05 2014