login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239986 T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4 13

%I

%S 1,1,2,1,3,3,1,4,6,4,1,5,13,16,7,1,6,22,56,40,10,1,7,38,171,261,84,15,

%T 1,8,65,530,1391,935,208,24,1,9,107,1495,7113,9079,4113,474,35,1,10,

%U 169,4059,31226,83658,70107,16724,1047,54,1,11,257,10121,131242,652346

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to zero plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4

%C Table starts

%C ..1....1......1........1..........1............1............1............1

%C ..2....3......4........5..........6............7............8............9

%C ..3....6.....13.......22.........38...........65..........107..........169

%C ..4...16.....56......171........530.........1495.........4059........10121

%C ..7...40....261.....1391.......7113........31226.......131242.......514539

%C .10...84....935.....9079......83658.......652346......4803152.....33097266

%C .15..208...4113....70107....1174822.....16721012....226886115...2823199343

%C .24..474..16724...514297...15307425....381369904...9004871354.198719581101

%C .35.1047..63746..3533132..192702130...9009351655.404795616742

%C .54.2530.275188.27478686.2733573580.233083355837

%H R. H. Hardin, <a href="/A239986/b239986.txt">Table of n, a(n) for n = 1..128</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2) +2*a(n-3)

%F k=2: a(n) = 2*a(n-2) +10*a(n-3) -a(n-4) -5*a(n-5) -15*a(n-6) +a(n-7) +4*a(n-8) +2*a(n-9) +10*a(n-10) +5*a(n-11) -6*a(n-13)

%F Empirical for row n:

%F n=1: a(n) = 1

%F n=2: a(n) = n + 1

%F n=3: a(n) = (1/24)*n^4 - (1/4)*n^3 + (71/24)*n^2 - (43/4)*n + 23 for n>3

%F n=4: [polynomial of degree 10] for n>12

%F n=5: [polynomial of degree 24] for n>31

%F n=6: [polynomial of degree 55] for n>73

%e Some solutions for n=4 k=4

%e ..3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0....3..0..0..0

%e ..3..1..3..0....2..3..0..3....3..1..3..0....2..1..0..0....2..1..0..0

%e ..3..1..2..1....2..0..1..2....3..2..0..3....2..0..3..3....2..0..3..0

%e ..2..1..0..0....3..0..0..1....2..3..0..3....3..2..2..2....2..0..0..3

%Y Column 1 is A159288

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Mar 30 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 12:40 EDT 2021. Contains 347477 sequences. (Running on oeis4.)