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.

Showing 1-6 of 6 results.

A295035 Number of nX3 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.

Original entry on oeis.org

4, 29, 140, 741, 3853, 19956, 104096, 541775, 2819027, 14671776, 76356631, 397392690, 2068192977, 10763659993, 56018290276, 291541126302, 1517293977155, 7896590852333, 41096944195828, 213884557644749, 1113138825391146
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2017

Keywords

Comments

Column 3 of A295040.

Examples

			Some solutions for n=7
..1..1..0. .1..0..0. .0..0..0. .0..0..1. .0..1..0. .1..1..0. .0..0..0
..0..0..0. .1..0..0. .1..1..1. .1..0..1. .0..1..0. .1..0..1. .0..0..1
..1..1..0. .1..1..0. .0..0..1. .1..1..0. .0..1..0. .0..1..1. .0..1..1
..0..0..0. .0..0..1. .0..0..0. .0..0..0. .0..1..0. .0..1..0. .1..1..0
..0..0..0. .0..0..1. .1..1..0. .1..1..1. .1..0..1. .0..1..1. .1..0..1
..1..1..0. .1..1..0. .0..1..0. .0..0..0. .1..0..1. .1..0..1. .0..0..1
..1..0..0. .0..0..0. .0..0..0. .0..0..0. .1..1..1. .1..0..1. .0..0..1
		

Crossrefs

Cf. A295040.

Programs

  • Maple
    q:= proc(a,b) local r,s,t,M,i;
       s:= floor((a-1)/8);
       if s <> (b-1) mod 8 then return 0 fi;
       s:= convert(s+8,base,2);
       r:= convert(8+floor((b-1)/8),base,2);
       t:= convert(8+ ((a-1) mod 8),base,2);
       M:= Vector(3);
       if s[1] = 1 and s[2] = 1 then M[1]:= 1; M[2]:= 1 fi;
       if s[2]=1 and s[3]=1 then M[2]:= M[2]+1; M[3]:= 1 fi;
       for i from 1 to 3 do if s[i]=1 then
         M[i]:= M[i]+r[i]+t[i];
         if M[i] = 0 or M[i]>2 then return 0 fi;
       fi od;
       1
    end proc:
    T:= Matrix(64,64, q);
    u:= Vector[row](64):
    v:= Vector(64):
    for i from 0 to 7 do u[8*i+1]:= 1; v[i+1]:= 1;
    od:
    seq(u . T^n . v, n = 1 .. 100); # Robert Israel, Nov 12 2017

Formula

Empirical: a(n) = 4*a(n-1) +2*a(n-2) +17*a(n-3) +18*a(n-4) +53*a(n-5) -23*a(n-6) -38*a(n-7) +52*a(n-8) -19*a(n-9) -14*a(n-10) +16*a(n-11) -11*a(n-12) +a(n-14) -a(n-15)
Empirical formula confirmed by Robert Israel, Nov 12 2017 (see link).

A295036 Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.

Original entry on oeis.org

7, 87, 741, 6686, 59126, 528282, 4738235, 42321441, 378112132, 3379951089, 30211913537, 270034246073, 2413553512560, 21572510872955, 192816992434886, 1723410496604699, 15403947766639408, 137681484497162534
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2017

Keywords

Comments

Column 4 of A295040.

Examples

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

Crossrefs

Cf. A295040.

Formula

Empirical: a(n) = 6*a(n-1) +11*a(n-2) +110*a(n-3) +218*a(n-4) +381*a(n-5) -1782*a(n-6) -2295*a(n-7) +4944*a(n-8) +5724*a(n-9) -6097*a(n-10) -7938*a(n-11) -1252*a(n-12) +14108*a(n-13) +11254*a(n-14) -22229*a(n-15) -16840*a(n-16) +27235*a(n-17) -25020*a(n-18) +11308*a(n-19) +6762*a(n-20) -1639*a(n-21) +2585*a(n-22) +642*a(n-23) -2303*a(n-24) -429*a(n-25) +661*a(n-26) -215*a(n-27) +117*a(n-28) -14*a(n-29) -36*a(n-30) +7*a(n-31) +4*a(n-32) +2*a(n-33) -a(n-34)

A295037 Number of nX5 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.

Original entry on oeis.org

12, 280, 3853, 59126, 898493, 13706771, 209181266, 3184995895, 48548926944, 740019106008, 11277857830329, 171883749077632, 2619682437092951, 39926222792932513, 608509663116604097, 9274219880373144746
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2017

Keywords

Comments

Column 5 of A295040.

Examples

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

Crossrefs

Cf. A295040.

Formula

Empirical recurrence of order 91 (see link above)

A295038 Number of nX6 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.

Original entry on oeis.org

21, 876, 19956, 528282, 13706771, 355281224, 9248214732, 240292442848, 6243986963713, 162252303626409, 4216381439247094, 109570922468132003, 2847344541437365138, 73992200911927723171, 1922796991924326509127
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2017

Keywords

Comments

Column 6 of A295040.

Examples

			Some solutions for n=3
..1..0..0..1..0..0. .1..1..0..1..1..1. .0..0..0..1..0..1. .0..0..0..0..0..1
..1..0..0..1..1..0. .1..0..1..0..0..1. .1..1..0..1..0..1. .0..1..0..1..0..1
..1..0..0..0..1..0. .0..0..1..0..0..0. .0..1..0..0..0..0. .1..1..0..1..0..0
		

Crossrefs

Cf. A295040.

A295039 Number of nX7 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.

Original entry on oeis.org

37, 2735, 104096, 4738235, 209181266, 9248214732, 411280569141, 18227207589288, 807975522778623, 35828949243544333, 1588724655137268304, 70444327993290622210, 3123514826860958239480, 138498446900583005504125
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2017

Keywords

Comments

Column 7 of A295040.

Examples

			Some solutions for n=3
..0..0..0..1..1..1..0. .0..0..1..1..0..0..0. .1..1..0..0..0..0..0
..0..0..0..0..0..1..0. .1..0..0..0..0..1..1. .1..1..0..1..1..1..0
..1..1..0..0..0..1..0. .1..1..1..1..0..0..1. .0..0..0..0..0..1..1
		

Crossrefs

Cf. A295040.

A295034 Number of n X n 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1's.

Original entry on oeis.org

1, 10, 140, 6686, 898493, 355281224, 411280569141, 1377458578461777, 13439667379225204666, 381706479329790703639253, 31542814403404743062254741113, 7585239934805237805543429969496485
Offset: 1

Views

Author

R. H. Hardin, Nov 12 2017

Keywords

Examples

			Some solutions for n=4:
..0..1..1..0. .1..1..1..1. .1..0..0..0. .0..0..0..1. .1..0..1..1
..0..0..1..1. .1..0..0..1. .1..0..0..0. .0..0..1..1. .1..0..1..0
..1..0..0..1. .0..0..0..0. .1..0..0..0. .1..0..1..0. .0..0..0..1
..1..1..0..1. .0..1..1..1. .0..0..0..0. .1..1..0..0. .0..1..1..1
		

Crossrefs

Diagonal of A295040.
Showing 1-6 of 6 results.