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 1-2 of 2 results.

A140252 Inverse binomial transform of A140420.

Original entry on oeis.org

0, 1, 1, 7, 7, 31, 31, 127, 127, 511, 511, 2047, 2047, 8191, 8191, 32767, 32767, 131071, 131071, 524287, 524287, 2097151, 2097151, 8388607, 8388607, 33554431, 33554431, 134217727, 134217727, 536870911, 536870911
Offset: 0

Views

Author

Paul Curtz, Jun 23 2008

Keywords

Comments

Also, the decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 673", based on the 5-celled von Neumann neighborhood, initialized with a single black (ON) cell at stage zero. - Robert Price, Jul 23 2017

References

  • S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

Links

Programs

  • Mathematica
    Join[{0},LinearRecurrence[{1,4,-4},{1,1,7},30]] (* Harvey P. Dale, May 28 2012 *)

Formula

a(2n+1) = a(2n+2)= A083420(n).
a(n+1)-2a(n) = (-1)^n*A014551(n), n>0.
a(n+1)-2a(n)-1 = 2*(-1)^n*A131577(n).
O.g.f.: x(1+2x^2)/((2x-1)(1+2x)(x-1)). - R. J. Mathar, Aug 02 2008
a(n) = a(n-1)+4*a(n-2)-4*a(n-3), a(0)=0, a(1)=1, a(2)=1, a(3)=7. - Harvey P. Dale, May 28 2012

Extensions

Edited and extended by R. J. Mathar, Aug 02 2008

A092438 Sequence arising from enumeration of domino tilings of Aztec Pillow-like regions.

Original entry on oeis.org

0, 2, 6, 26, 90, 302, 966, 3026, 9330, 28502, 86526, 261626, 788970, 2375102, 7141686, 21457826, 64439010, 193448102, 580606446, 1742343626, 5228079450, 15686335502, 47063200806, 141197991026, 423610750290, 1270865805302
Offset: 0

Views

Author

Christopher Hanusa (chanusa(AT)math.washington.edu), Mar 24 2004

Keywords

Examples

			a(3) = (3^4+(-1)^4)/2-2^4+1 = 26.

References

  • J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see Problem 13).

Links

Crossrefs

Cf. A046717, A092437-A092443, A140420.

Formula

a(n) = A092437(n, n+1).
a(n) = A046717(n+1)-2^(n+1)+1.
a(n) = (3^(n+1)+(-1)^(n+1))/2-2^(n+1)+1.
From R. J. Mathar, Apr 21 2010: (Start)
a(n) = +5*a(n-1) -5*a(n-2) -5*a(n-3) +6*a(n-4) = 2*A140420(n).
G.f.: -2*x*(1-2*x+3*x^2) / ( (x-1)*(3*x-1)*(2*x-1)*(1+x) ). (End)
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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