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.

User: Jeff Bowermaster

Jeff Bowermaster's wiki page.

Jeff Bowermaster has authored 2 sequences.

A329279 Number of distinct tilings of a 2n X 2n square with 1 x n polyominoes.

Original entry on oeis.org

1, 9, 11, 19, 22, 33, 37, 51, 56, 73, 79, 99, 106, 129, 137, 163, 172, 201, 211, 243, 254, 289, 301, 339, 352, 393, 407, 451, 466, 513, 529, 579, 596, 649, 667, 723, 742, 801, 821, 883, 904, 969, 991, 1059, 1082, 1153, 1177, 1251, 1276, 1353, 1379, 1459, 1486, 1569, 1597, 1683, 1712, 1801, 1831
Offset: 1

Views

Author

Jeff Bowermaster, Nov 11 2019

Keywords

Comments

The positions of n X n subsquares greatly restricts which permutations are possible, simplifying finding solutions. a(n+1) - a(n) = A014682 (n+2), where A014682 is the Collatz function, except a(2)-a(1) = 8 and A014682(4) = 5.

Links

Crossrefs

Cf. A014682, A060312, A058331 (bisection).

Programs

  • PARI
    a(n) = if(n==1,1,if(n%2,(n^2+3*n)/2+2,(n^2+4*n)/2+3))

Formula

For even n, a(n) = (n^2+4n)/2+3; for odd n, a(n) = (n^2+3n)/2+2 ; a(1) = 1.

A328020 Number of distinct tilings of an n X n square with free n-polyominoes.

Original entry on oeis.org

1, 1, 2, 22, 515, 56734, 19846102, 23437350133
Offset: 1

Views

Author

Jeff Bowermaster, Oct 01 2019

Keywords

Links

Crossrefs

Cf. A172477, A268427, A291806.

Extensions

a(7) from Peter Kagey, Oct 10 2019, based on the Stack Exchange link.
a(8) from Christian Sievers, Oct 13 2019, based on the Stack Exchange link.

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