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 1-7 of 7 results.

A255287 Number of 1's in expansion of F^n mod 3, where F = 1/(x*y)+1/y+x/y+1/x+x+y/x+y+x*y.

Original entry on oeis.org

1, 8, 8, 8, 64, 52, 8, 64, 101, 8, 64, 64, 64, 512, 404, 52, 416, 448, 8, 64, 233, 64, 512, 700, 101, 808, 992, 8, 64, 64, 64, 512, 416, 64, 512, 808, 64, 512, 512, 512, 4096, 3220, 404, 3232, 3224, 52, 416, 832, 416, 3328
Offset: 0

Views

Author

N. J. A. Sloane, Feb 21 2015

Keywords

Comments

A255287 and A255288 together are a mod 3 analog of A160239.

Examples

			The pairs [no. of 1's, no. of 2's] are [1, 0], [8, 0], [8, 13], [8, 0], [64, 0], [52, 32], [8, 13], [64, 104], [101, 112], [8, 0], [64, 0], [64, 104], [64, 0], [512, 0], [404, 184], [52, 32], [416, 256], [448, 296], [8, 13], [64, 104], [233, 208], [64, 104], [512, 832], [700, 836], [101, 112], [808, 896], [992, 1081], ...

Crossrefs

Cf. A160239, A255288-A255294.

Programs

  • Maple
    # C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F1:=1/(x*y)+1/y+x/y+1/x+x+y/x+y+x*y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F1,n))[1],n=0..60)];

A255288 Number of 2's in expansion of F^n mod 3, where F = 1/(x*y)+1/y+x/y+1/x+x+y/x+y+x*y.

Original entry on oeis.org

0, 0, 13, 0, 0, 32, 13, 104, 112, 0, 0, 104, 0, 0, 184, 32, 256, 296, 13, 104, 208, 104, 832, 836, 112, 896, 1081, 0, 0, 104, 0, 0, 256, 104, 832, 896, 0, 0, 832, 0, 0, 1400, 184, 1472, 1768, 32, 256, 932, 256, 2048, 2692, 296
Offset: 0

Views

Author

N. J. A. Sloane, Feb 21 2015

Keywords

Comments

A255287 and A255288 together are a mod 3 analog of A160239.

Examples

			The pairs [no. of 1's, no. of 2's] are [1, 0], [8, 0], [8, 13], [8, 0], [64, 0], [52, 32], [8, 13], [64, 104], [101, 112], [8, 0], [64, 0], [64, 104], [64, 0], [512, 0], [404, 184], [52, 32], [416, 256], [448, 296], [8, 13], [64, 104], [233, 208], [64, 104], [512, 832], [700, 836], [101, 112], [808, 896], [992, 1081], ...

Crossrefs

Cf. A160239, A255287-A255294.

Programs

  • Maple
    # C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F1:=1/(x*y)+1/y+x/y+1/x+x+y/x+y+x*y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F1,n))[2],n=0..60)];

A255289 Number of 1's in expansion of F^n mod 3, where F = 1/(x*y)+2/y+x/y+2/x+2*x+y/x+2*y+x*y.

Original entry on oeis.org

1, 4, 12, 4, 32, 48, 12, 84, 117, 4, 32, 84, 32, 256, 300, 48, 336, 324, 12, 84, 225, 84, 672, 792, 117, 852, 876, 4, 32, 84, 32, 256, 336, 84, 672, 852, 32, 256, 672, 256, 2048, 2316, 300, 2352, 2448, 48, 336, 900, 336
Offset: 0

Views

Author

N. J. A. Sloane, Feb 21 2015

Keywords

Comments

A255289 and A255290 together are a second mod 3 analog of A160239.

Examples

			The pairs [no. of 1's, no. of 2's] are [1, 0], [4, 4], [12, 9], [4, 4], [32, 32], [48, 36], [12, 9], [84, 84], [117, 96], [4, 4], [32, 32], [84, 84], [32, 32], [256, 256], [300, 288], [48, 36], [336, 336], [324, 420], [12, 9], [84, 84], [225, 216], [84, 84], [672, 672], [792, 744], [117, 96], [852, 852], [876, 1197], ...

Crossrefs

Cf. A160239, A255287-A255294.

Programs

  • Maple
    # C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F2:=1/(x*y)+2/y+x/y+2/x+2*x+y/x+2*y+x*y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F2,n))[1],n=0..60)];

A255290 Number of 2's in expansion of F^n mod 3, where F = 1/(x*y)+2/y+x/y+2/x+2*x+y/x+2*y+x*y.

Original entry on oeis.org

0, 4, 9, 4, 32, 36, 9, 84, 96, 4, 32, 84, 32, 256, 288, 36, 336, 420, 9, 84, 216, 84, 672, 744, 96, 852, 1197, 4, 32, 84, 32, 256, 336, 84, 672, 852, 32, 256, 672, 256, 2048, 2304, 288, 2352, 2544, 36, 336, 864, 336, 2688
Offset: 0

Views

Author

N. J. A. Sloane, Feb 21 2015

Keywords

Comments

A255289 and A255290 together are a second mod 3 analog of A160239.

Examples

			The pairs [no. of 1's, no. of 2's] are [1, 0], [4, 4], [12, 9], [4, 4], [32, 32], [48, 36], [12, 9], [84, 84], [117, 96], [4, 4], [32, 32], [84, 84], [32, 32], [256, 256], [300, 288], [48, 36], [336, 336], [324, 420], [12, 9], [84, 84], [225, 216], [84, 84], [672, 672], [792, 744], [117, 96], [852, 852], [876, 1197], ...

Crossrefs

Cf. A160239, A255287-A255294.

Programs

  • Maple
    # C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F2:=1/(x*y)+2/y+x/y+2/x+2*x+y/x+2*y+x*y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F2,n))[2],n=0..60)];

A255291 Number of 1's in expansion of F^n mod 3, where F = 1/x+1+x+1/y+y.

Original entry on oeis.org

1, 5, 4, 5, 25, 12, 4, 20, 69, 5, 25, 20, 25, 125, 52, 12, 60, 281, 4, 20, 97, 20, 100, 353, 69, 345, 448, 5, 25, 20, 25, 125, 60, 20, 100, 345, 25, 125, 100, 125, 625, 252, 52, 260, 1341, 12, 60, 381, 60, 300, 1413, 281, 1405
Offset: 0

Views

Author

N. J. A. Sloane, Feb 21 2015

Keywords

Comments

A255291 and A255292 together are a mod 3 analog of A072272.

Examples

			The pairs [no. of 1's, no. of 2's] are [1, 0], [5, 0], [4, 9], [5, 0], [25, 0], [12, 37], [4, 9], [20, 45], [69, 44], [5, 0], [25, 0], [20, 45], [25, 0], [125, 0], [52, 177], [12, 37], [60, 185], [281, 156], [4, 9], [20, 45], [97, 72], [20, 45], [100, 225], [353, 228], [69, 44], [345, 220], [448, 573], [5, 0], [25, 0], [20, 45], ...

Crossrefs

Cf. A072272, A255288-A255294.

Programs

  • Maple
    # C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F3:=1/x+1+x+1/y+y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F3,n))[1],n=0..60)];

A255292 Number of 2's in expansion of F^n mod 3, where F = 1/x+1+x+1/y+y.

Original entry on oeis.org

0, 0, 9, 0, 0, 37, 9, 45, 44, 0, 0, 45, 0, 0, 177, 37, 185, 156, 9, 45, 72, 45, 225, 228, 44, 220, 573, 0, 0, 45, 0, 0, 185, 45, 225, 220, 0, 0, 225, 0, 0, 877, 177, 885, 716, 37, 185, 256, 185, 925, 788, 156, 780, 2281, 9
Offset: 0

Views

Author

N. J. A. Sloane, Feb 21 2015

Keywords

Comments

A255291 and A255292 together are a mod 3 analog of A072272.

Examples

			The pairs [no. of 1's, no. of 2's] are [1, 0], [5, 0], [4, 9], [5, 0], [25, 0], [12, 37], [4, 9], [20, 45], [69, 44], [5, 0], [25, 0], [20, 45], [25, 0], [125, 0], [52, 177], [12, 37], [60, 185], [281, 156], [4, 9], [20, 45], [97, 72], [20, 45], [100, 225], [353, 228], [69, 44], [345, 220], [448, 573], [5, 0], [25, 0], [20, 45], ...

Crossrefs

Cf. A072272, A255288-A255294.

Programs

  • Maple
    # C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F3:=1/x+1+x+1/y+y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F3,n))[2],n=0..60)];

A255293 Number of 1's in expansion of F^n mod 3, where F = 1/x+2+x+1/y+y.

Original entry on oeis.org

1, 4, 8, 4, 17, 29, 8, 37, 49, 4, 17, 37, 17, 76, 128, 29, 136, 196, 8, 37, 89, 37, 176, 292, 49, 260, 584, 4, 17, 37, 17, 76, 136, 37, 176, 260, 17, 76, 176, 76, 353, 605, 128, 613, 961, 29, 136, 332, 136, 653, 1105, 196
Offset: 0

Views

Author

N. J. A. Sloane, Feb 21 2015

Keywords

Comments

A255293 and A255294 together are a second mod 3 analog of A072272.

Examples

			The pairs [no. of 1's, no. of 2's] are [1, 0], [4, 1], [8, 5], [4, 1], [17, 8], [29, 20], [8, 5], [37, 28], [49, 64], [4, 1], [17, 8], [37, 28], [17, 8], [76, 49], [128, 101], [29, 20], [136, 109], [196, 241], [8, 5], [37, 28], [89, 80], [37, 28], [176, 149], [292, 289], [49, 64], [260, 305], [584, 437], [4, 1], [17, 8], [37, 28], ...

Crossrefs

Cf. A072272, A255287-A255294.

Programs

  • Maple
    # C3 Counts 1's and 2's
C3 := proc(f) local c,ix,iy,f2,i,t1,t2,n1,n2;
f2:=expand(f) mod 3; n1:=0; n2:=0;
if whattype(f2) = `+` then
t1:=nops(f2);
for i from 1 to t1 do t2:=op(i, f2); ix:=degree(t2, x); iy:=degree(t2, y);
c:=coeff(coeff(t2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; od: RETURN([n1,n2]);
else ix:=degree(f2, x); iy:=degree(f2, y);
c:=coeff(coeff(f2,x,ix),y,iy);
if (c mod 3) = 1 then n1:=n1+1; else n2:=n2+1; fi; RETURN([n1,n2]);
fi;
end;
F4:=1/x+2+x+1/y+y mod 3;
g:=(F,n)->expand(F^n) mod 3;
[seq(C3(g(F4,n))[1],n=0..60)];
Showing 1-7 of 7 results.

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