A034186 -id:A034186 - cp's OEIS frontend

A034184 Not necessarily symmetric n X 3 crossword puzzle grids.

1, 15, 111, 649, 3495, 18189, 93231, 474479, 2406621, 12187137, 61668609, 311938233, 1577602849, 7977940187, 40342860995, 204001993697, 1031568839407, 5216271035257, 26376744398811, 133377264694375

Offset: 1

Erich Friedman

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..200
Louis Marin, Counting Polyominoes in a Rectangle b X h, arXiv:2406.16413 [cs.DM], 2024. See p. 145.

Row 3 of A292357.
Column sums of A059679.
Cf. A001333, A034182, A034184, A034185, A034186, A034187.

Appears to obey a 9-term linear recurrence. - Ralf Stephan, May 05 2004

Empirical g.f.: -x*(x^8-x^7-2*x^6-9*x^5+14*x^4-11*x^3-6*x^2+5*x+1) / ((x-1)*(x^2+2*x-1)*(x^6-7*x^5+x^4+6*x^3-11*x^2+7*x-1)). - Colin Barker, Jun 09 2013

A034187 Not necessarily symmetric n X 4 crossword puzzle grids.

Original entry on oeis.org

1, 39, 649, 7943, 86995, 910667, 9339937, 94844591, 958363411, 9659847433, 97245624749, 978360244839, 9839915415611, 98949930968385, 994959069405031, 10004090931544495, 100586881489055547, 1011348141567934109

Offset: 1

Erich Friedman

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..200

Row 4 of A292357.
Column sums of A059680.
Cf. A001333, A034184, A034185, A034186, A034187.

Empirical: a(n) = 24*a(n-1) - 218*a(n-2) + 1009*a(n-3) - 2623*a(n-4) + 3513*a(n-5) - 142*a(n-6) - 7707*a(n-7) + 11632*a(n-8) - 4443*a(n-9) - 6736*a(n-10) + 9655*a(n-11) - 3714*a(n-12) - 1529*a(n-13) + 1550*a(n-14) - 597*a(n-15) + 1041*a(n-16) + 195*a(n-17) - 150*a(n-18) + 8*a(n-19) + a(n-20) for n > 20. - Andrew Howroyd, Oct 02 2017

Empirical: x *(-1 -15*x +69*x^2 +140*x^3 -1117*x^4 +1696*x^5 +186*x^6 -1351*x^7 -1715*x^8 +3376*x^9 -52*x^10 -1829*x^11 +905*x^12 -1748*x^13 +446*x^14 -241*x^15 -72*x^16 +35*x^17 +7*x^18 +x^19) / ( (x^2+2*x-1) *(x^6 -7*x^5 +x^4 +6*x^3 -11*x^2 +7*x -1) *(x^12 +13*x^11 -71*x^10 +7*x^9 -113*x^8 +22*x^7 +222*x^6 -210*x^5 -19*x^4 +97*x^3 -59*x^2 +15*x -1) ). - R. J. Mathar, Jun 07 2020

A034185 Number of symmetric n X 3 crossword puzzle grids.

Original entry on oeis.org

1, 3, 11, 21, 61, 111, 309, 565, 1563, 2859, 7907, 14459, 39991, 73117, 202227, 369729, 1022587, 1869581, 5170829, 9453757, 26146909, 47804041, 132214959, 241726811, 668560673, 1222320359, 3380656559, 6180808253, 17094691953, 31253992007, 86441342981

Offset: 1

Erich Friedman

nonn

Rules: all white squares are edge connected; at least 1 white square on every edge of grid; symmetric ones have 180-degree rotational symmetry.

Sean A. Irvine, Java program (github)

Cf. A001333, A034184, A034186, A034187.

a(23)-a(31) from Sean A. Irvine, Aug 07 2020

cp's OEIS Frontend

A034184 Not necessarily symmetric n X 3 crossword puzzle grids.

Views

Author

Keywords

Links

Crossrefs

Formula

A034187 Not necessarily symmetric n X 4 crossword puzzle grids.

Views

Author

Keywords

Links

Crossrefs

Formula

A034185 Number of symmetric n X 3 crossword puzzle grids.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions