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.

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A302336 Linear coefficient (in absolute value) of the quadratic polynomials giving the numbers of 2k-cycles in the n X n grid graph for n >= k-1.

Original entry on oeis.org

0, 2, 6, 28, 140, 740, 4056, 22904, 132344, 778832, 4652404, 28140536, 172021360, 1061153560, 6597813620, 41307119692, 260198053200, 1647958588568, 10488324116052, 67046234983840, 430300354820176, 2771678138269600, 17912347088664868, 116113406138798112
Offset: 1

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Author

Eric W. Weisstein, Apr 05 2018

Keywords

Examples

			Let p(k,n) be the number of 2k-cycles in the n X n grid graph for n >= k-1. p(k,n) are quadratic polynomials in n, with the first few given by:
  p(1,n) =      0,
  p(2,n) =      1 -      2*n +       n^2,
  p(3,n) =      4 -      6*n +     2*n^2,
  p(4,n) =     26 -     28*n +     7*n^2,
  p(5,n) =    164 -    140*n +    28*n^2,
  p(6,n) =   1046 -    740*n +   124*n^2,
  p(7,n) =   6672 -   4056*n +   588*n^2,
  p(8,n) =  42790 -  22904*n +  2938*n^2,
  p(9,n) = 275888 - 132344*n + 15268*n^2,
  ...
The linear coefficients give a(n), so the first few are 0, 2, 6, 28, 140, .... - _Eric W. Weisstein_, Apr 05 2018
		

Crossrefs

Cf. A302335 (constant coefficients).
Cf. A002931 (quadratic coefficients).

Formula

a(n) = 2*A006772(n). - Andrey Zabolotskiy, Nov 09 2018

Extensions

Terms a(12) and beyond added using data from A006772 by Andrey Zabolotskiy, Feb 10 2022

A006773 Sum of squared spans of 2n-step polygons on square lattice.

Original entry on oeis.org

0, 1, 5, 30, 186, 1164, 7344, 46732, 299604, 1932900, 12537542, 81705782, 534663812, 3511466838, 23136724382, 152888000934, 1012925595468, 6726766841438, 44767880394634, 298522284224824, 1994187071224056, 13343458013982572, 89420609914983270, 600088861692380354, 4032377457462571694, 27129080022839863318, 182726605700552001998
Offset: 1

Views

Author

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A006772.

Extensions

Name corrected, more terms from Andrey Zabolotskiy, Nov 09 2018
Showing 1-2 of 2 results.