A302312 Number of 4Xn 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

8, 10, 33, 66, 194, 663, 2048, 5790, 17761, 58980, 191180, 596347, 1907378, 6288532, 20577053, 66405860, 215990588, 709815637, 2327287890, 7595046870, 24844917677, 81549601926, 267490606860, 876047158691, 2871110160412, 9420069102786

Offset

1,1

Comments

Row 4 of A302309.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) +5*a(n-2) +60*a(n-4) -131*a(n-5) -353*a(n-6) +10*a(n-7) -1175*a(n-8) +3055*a(n-9) +7872*a(n-10) +147*a(n-11) +12947*a(n-12) -33227*a(n-13) -87331*a(n-14) -9250*a(n-15) -93900*a(n-16) +187065*a(n-17) +567276*a(n-18) +117942*a(n-19) +450056*a(n-20) -548959*a(n-21) -2334141*a(n-22) -730683*a(n-23) -1443723*a(n-24) +687058*a(n-25) +6323246*a(n-26) +2755222*a(n-27) +3362249*a(n-28) +657022*a(n-29) -11137465*a(n-30) -6733801*a(n-31) -5922943*a(n-32) -4829865*a(n-33) +11295211*a(n-34) +9594872*a(n-35) +7037564*a(n-36) +9773770*a(n-37) -4045646*a(n-38) -6292677*a(n-39) -2960406*a(n-40) -7716783*a(n-41) -3109708*a(n-42) +290519*a(n-43) -336302*a(n-44) +1567545*a(n-45) +1178128*a(n-46) +451089*a(n-47) +464276*a(n-48) -213008*a(n-49) -10214*a(n-50) -148486*a(n-51) -128582*a(n-52) +12396*a(n-53) -23456*a(n-54) +25976*a(n-55) +10232*a(n-56) -212*a(n-57) +1968*a(n-58) -1008*a(n-59) -160*a(n-60) +64*a(n-61) for n>64

Example

Some solutions for n=5
..0..1..0..0..1. .0..1..0..1..0. .0..0..1..0..1. .0..1..1..1..0
..1..1..0..1..0. .1..1..0..1..0. .1..1..1..0..1. .1..1..1..0..1
..0..1..0..1..0. .0..1..0..1..1. .0..0..0..0..1. .0..1..1..0..1
..0..0..0..1..0. .0..0..0..1..0. .0..1..1..0..1. .0..1..0..1..1

Crossrefs

Cf. A302309.

Sequence in context: A126807 A230110 A223587 * A245199 A303042 A242506

Adjacent sequences: A302309 A302310 A302311 * A302313 A302314 A302315

Keyword

nonn

Author

R. H. Hardin, Apr 05 2018

Status

approved