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.

A302309 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 5, 11, 6, 8, 8, 21, 13, 10, 16, 13, 31, 26, 33, 21, 32, 21, 113, 48, 66, 58, 42, 64, 34, 363, 121, 194, 153, 153, 86, 128, 55, 813, 275, 663, 445, 380, 336, 179, 256, 89, 1751, 600, 2048, 1595, 1271, 1090, 937, 370, 512, 144, 5001, 1296, 5790, 4772, 5715
Offset: 1

Views

Author

R. H. Hardin, Apr 05 2018

Keywords

Comments

Table starts
...1...2....3....5.....8.....13......21.......34........55.........89
...2...3...11...21....31....113.....363......813......1751.......5001
...4...6...13...26....48....121.....275......600......1296.......2998
...8..10...33...66...194....663....2048.....5790.....17761......58980
..16..21...58..153...445...1595....4772....15249.....49634.....166329
..32..42..153..380..1271...5715...18992....70289....276303....1198933
..64..86..336.1090..3915..18990...76642...360898...1695748....9408402
.128.179..937.3120.12420..73663..364922..2150420..13123505...95790405
.256.370.2449.9130.42897.312122.1991487.15392485.124691962.1235540899

Examples

			Some solutions for n=5 k=4
..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..0. .0..1..0..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .0..0..0..0. .1..0..0..1. .1..1..0..0
..0..1..0..1. .0..1..0..1. .1..1..1..0. .1..0..1..0. .0..1..0..1
..0..1..1..1. .0..1..1..1. .1..0..1..0. .1..0..1..0. .0..1..0..1
		

Crossrefs

Column 1 is A000079(n-1).
Column 2 is A240513.
Row 1 is A000045(n+1).

Formula

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)
k=3: [order 13] for n>16
k=4: [order 60] for n>61
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) +12*a(n-4) -16*a(n-5) for n>6
n=3: [order 15] for n>16
n=4: [order 61] for n>64