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.
Needs["LinearAlgebra`MatrixManipulation`"] Remove[mat] step[sa[rules1_, {dim1_, dim1_}], sa[rules2_, {dim2_, dim2_}]] := sa[Join[rules2, rules1 /. {x_Integer, y_Integer} -> {x + dim2, y}, rules1 /. {x_Integer, y_Integer} -> {x, y + dim2}], {dim1 + dim2, dim1 + dim2}] mat[0] = sa[{{1, 1} -> 1}, {1, 1}]; mat[1] = sa[{{1, 1} -> 1, {1, 2} -> 1, {2, 1} -> 1}, {2, 2}]; mat[n_] := mat[n] = step[mat[n - 2], mat[n - 1]]; A[n_] := mat[n] /. sa -> SparseArray; F[n_] := MatrixPower[A[n], n + 1][[1, 1]]; (* Mark McClure (mcmcclur(AT)bulldog.unca.edu), Mar 19 2006 *)
$RecursionLimit = 1000; Clear[a, b]; b[n_, l_List] := b[n, l] = Module[{m=Min[l], k}, If[m>0, b[n-m, l-m], If[n == 0, 1, k=Position[l, 0, 1, 1][[1, 1]]; b[n, ReplacePart[l, k -> 1]] + If[n>1 && k 2, k+1 -> 2}]], 0]]]]; a[n_] := a[n] = If[n<2, 1, b[n, Table[0, {n}]]]; Table[Print[a[n]]; a[n], {n, 0, 17}] (* Jean-François Alcover, Dec 11 2014, after Alois P. Heinz *)
a[n_] := With[{sets = Select[Tuples[{0, 1}, n], Count[#*RotateLeft[#], 1] == 0 &]}, Tr[MatrixPower[Table[Boole[Count[s1*s2, 1] == 0], {s1, sets}, {s2, sets}], n]]];
Table[a[n], {n, 1, 10}] (* Pjotr Buys, Jun 07 2023 *)
Neighbors for n=4: o--o--o--o | /| /| /| |/ |/ |/ | o--o--o--o | /| /| /| |/ |/ |/ | o--o--o--o | /| /| /| |/ |/ |/ | o--o--o--o
a:= proc(n) option remember; local b; b:=
proc(n, l) option remember; local k;
if n<2 then 1
elif min(l[])>0 then b(n-1, map(h->h-1, l))
else for k while l[k]>0 do od; b(n, subsop(k=1, l))+
`if`(n>1 and kAlois P. Heinz, Aug 26 2013
$RecursionLimit = 1000; a[n0_] := a[n0] = Module[{b}, b[n_, l_List] := b[n, l] = Module[{k}, Which[n<2, 1, Min[l]>0, b[n-1, l-1], True, For[k = 1, l[[k]] > 0, k++]; b[n, ReplacePart[l, k -> 1]] + If[n>1 && k 2, k+1 -> 1}]], 0]]]; b[n0+1, Array[0&, n0+1]]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 24 2015, after Alois P. Heinz *)
Table starts: ======================================================== n\k| 1 2 3 4 5 6 7 ---|---------------------------------------------------- 1 | 2 3 5 8 13 21 34 ... 2 | 3 7 17 41 99 239 577 ... 3 | 5 17 63 227 827 2999 10897 ... 4 | 8 41 227 1234 6743 36787 200798 ... 5 | 13 99 827 6743 55447 454385 3729091 ... 6 | 21 239 2999 36787 454385 5598861 69050253 ... 7 | 34 577 10897 200798 3729091 69050253 1280128950 ... ... - _Andrew Howroyd_, Jun 06 2017 a(2,2)=7: 11 11 11 10 10 01 01 11 10 01 11 01 11 10
step(v, S)={vector(#v, i, sum(j=1, #v, v[j]*!bitand(S[i], S[j])))}
mkS(k)={select(b->!bitand(b,b>>1), [0..2^k-1])}
T(n,k)={my(S=mkS(k), v=vector(#S, i, i==1)); for(n=1, n, v=step(v,S)); vecsum(v)} \\ Andrew Howroyd, Dec 24 2019
Neighbors for n=4: o o o o | | | | | | | | o o o o | | | | | | | | o o o o | | | | | | | | o o o o
[Fibonacci(n+2)^n: n in [0..13]]; // Bruno Berselli, Mar 28 2012
Table[Fibonacci[n+2]^n, {n, 0, 100}]
makelist(fib(n+2)^n, n, 0, 14);
a(n)=fibonacci(n+2)^n \\ Charles R Greathouse IV, Mar 28 2012
neighbors for n=4: .|/ |/ |/ |/ -o--o--o--o- /| /| /| /| .|/ |/ |/ |/ -o--o--o--o- /| /| /| /| .|/ |/ |/ |/ -o--o--o--o- /| /| /| /| .|/ |/ |/ |/ -o--o--o--o- /| /| /| /|
Neighbors for n=4: | | | | o o o o | | | | | | | | o o o o | | | | | | | | o o o o | | | | | | | | o o o o | | | |
[Lucas(n)^n: n in [1..15]]; // Vincenzo Librandi, Mar 15 2014
a:= n-> (<<0|1>, <1|1>>^n. <<2, 1>>)[1$2]^n: seq(a(n), n=1..15); # Alois P. Heinz, Aug 01 2021
Table[LucasL[n]^n,{n,15}] (* Harvey P. Dale, Mar 13 2014 *)
Neighbors for n=4 (dots represent spaces): . o..o..o..o ...\/ \/ \/ .../\ /\ /\ . o..o..o..o ...\/ \/ \/ .../\ /\ /\ . o..o..o..o ...\/ \/ \/ .../\ /\ /\ . o..o..o..o
Comments