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 1-4 of 4 results.

A271486 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,23).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 11, 16, 22, 30, 43, 60, 82, 113, 162, 224, 306, 435, 610, 836, 1168, 1637, 2282, 3120, 4399, 6131, 8522, 11812, 16561, 22933, 31810, 44468, 62335, 85639, 119452, 167281, 233169, 320747, 449700, 626513, 872175
Offset: 0

Views

Author

N. J. A. Sloane, Apr 13 2016

Keywords

Links

Crossrefs

For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.

Programs

  • Maple
    A271486T := proc(n)
    option remember;
    local an ;
    if n = 1 then
        [1,1,1] ;
    else
        an := procname(floor(n/2)) ;
        if type(n,'even') then
            # apply F0
            [op(1,an)+op(3,an),op(3,an),op(2,an)] ;
        else
            # apply F1
            [op(1,an),op(1,an)+op(3,an),op(2,an)] ;
        end if;
    end if;
end proc:
A271486 := proc(n)
    local a,l,nmax;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        nmax := max( op(A271486T(l)) );
        a := max(a,nmax) ;
    end do:
    a ;
end proc: # R. J. Mathar, Apr 16 2016
  • Mathematica
    A271487T[n_] := A271487T[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = A271487T[Floor[n/2]]; If[EvenQ[n], {an[[1]] + an[[3]], an[[3]], an[[2]]}, {an[[1]], an[[1]] + an[[3]], an[[2]]}]]];
a[n_] := a[n] = Module[{a = 0, l, nMax}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, nMax = Max[A271487T[l]]; a = Max[a, nMax]]; a];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* Jean-François Alcover, Nov 17 2017, after R. J. Mathar *)

Extensions

a(20)-a(40) from Lars Blomberg, Jan 08 2018

A271485 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,e).

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 16, 25, 36, 56, 81, 126, 182, 283, 409, 636, 919, 1429, 2065, 3211, 4640, 7215, 10426, 16212, 23427, 36428, 52640, 81853, 118281, 183922, 265775, 413269, 597191, 928607, 1341876, 2086561, 3015168, 4688460, 6775021, 10534874, 15223334
Offset: 0

Views

Author

N. J. A. Sloane, Apr 13 2016

Keywords

Links

Crossrefs

For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.

Programs

  • Maple
    A271485T := proc(n)
    option remember;
    local an ;
    if n = 1 then
        [1,1,1] ;
    else
        an := procname(floor(n/2)) ;
        if type(n,'even') then
            # apply F0
            [op(1,an)+op(3,an),op(3,an),op(2,an)] ;
        else
            # apply F1
            [op(1,an),op(2,an),op(1,an)+op(3,an)] ;
        end if;
    end if;
end proc:
A271485 := proc(n)
    local a,l,nmax;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        nmax := max( op(A271485T(l)) );
        a := max(a,nmax) ;
    end do:
    a ;
end proc: # R. J. Mathar, Apr 16 2016
  • Mathematica
    A271487T[n_] := A271487T[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = A271487T[Floor[n/2]]; If[EvenQ[n], {an[[1]] + an[[3]], an[[3]], an[[2]]}, {an[[1]], an[[2]], an[[1]] + an[[3]]}]]];
a[n_] := a[n] = Module[{a = 0, l, nMax}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, nMax = Max[A271487T[l]]; a = Max[a, nMax]]; a];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* Jean-François Alcover, Nov 17 2017, after R. J. Mathar *)

Formula

Conjectures from Colin Barker, Apr 16 2016: (Start)
a(n) = 2*a(n-2)+a(n-4)-a(n-6) for n>5.
G.f.: (1+x)*(1+x-x^2)*(1+x^2) / (1-2*x^2-x^4+x^6).
(End)

Extensions

a(20)-a(40) from Lars Blomberg, Jan 08 2018

A271487 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,132).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 11, 17, 23, 32, 48, 65, 90, 136, 184, 255, 385, 521, 722, 1090, 1475, 2044, 3086, 4176, 5787, 8737, 11823, 16384, 24736, 33473, 46386, 70032, 94768, 131327, 198273, 268305, 371810, 561346, 759619, 1052660, 1589270
Offset: 0

Views

Author

N. J. A. Sloane, Apr 13 2016

Keywords

Links

Crossrefs

For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.

Programs

  • Maple
    A271487T := proc(n)
    option remember;
    local an ;
    if n = 1 then
        [1,1,1] ;
    else
        an := procname(floor(n/2)) ;
        if type(n,'even') then
            # apply F0
            [op(1,an)+op(3,an),op(3,an),op(2,an)] ;
        else
            # apply F1
            [op(2,an),op(1,an)+op(3,an),op(1,an)] ;
        end if;
    end if;
end proc;
A271487 := proc(n)
    local a,l,nmax;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        nmax := max( op(A271487T(l)) );
        a := max(a,nmax) ;
    end do:
    a ;
end proc: # R. J. Mathar, Apr 16 2016
  • Mathematica
    A271487T[n_] := A271487T[n] = Module[{an}, If[n == 1 , {1, 1, 1}, an = A271487T[Floor[n/2]]; If[EvenQ[n], {an[[1]] + an[[3]], an[[3]], an[[2]]}, {an[[2]], an[[1]] + an[[3]], an[[1]]}]]];
a[n_] := a[n] = Module[{a = 0, l, nMax}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, nMax = Max[A271487T[l]]; a = Max[a, nMax]]; a];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 24}] (* Jean-François Alcover, Nov 17 2017, after R. J. Mathar *)

Formula

Conjectures from Colin Barker, Apr 16 2016: (Start)
a(n) = 2*a(n-3)+2*a(n-6)+a(n-9) for n>9.
G.f.: (1+x)*(1+x+2*x^2+2*x^4+x^6+x^8) / (1-2*x^3-2*x^6-x^9).
(End)

Extensions

More terms from Jean-François Alcover, Nov 17 2017
a(25)-a(40) from Lars Blomberg, Jan 08 2018

A271489 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,132,e).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 10, 13, 18, 25, 34, 46, 64, 85, 117, 163, 217, 298, 415, 553, 759, 1057, 1408, 1933, 2692, 3586, 4923, 6856, 9133, 12538, 17461, 23260, 31932, 44470, 59239, 81325, 113257, 150871, 207120, 288445, 384241
Offset: 0

Views

Author

N. J. A. Sloane, Apr 13 2016

Keywords

Links

Crossrefs

For sequences mentioned in Conjecture 5.8 of Amburg et al. (2015) see A271485, A000930, A271486, A271487, A271488, A164001, A000045, A271489.

Programs

  • Maple
    A271489T := proc(n)
    option remember;
    local an,nrecur ;
    if n = 1 then
        [1,1,1] ;
    else
        an := procname(floor(n/2)) ;
        if type(n,'even') then
            # apply F0
            [op(3,an),op(1,an)+op(3,an),op(2,an)] ;
        else
            # apply F1
            [op(1,an),op(2,an),op(1,an)+op(3,an)] ;
        end if;
    end if;
end proc;
A271489 := proc(n)
    local a,l,nmax;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        nmax := max( op(A271489T(l)) );
        a := max(a,nmax) ;
    end do:
    a ;
end proc: # R. J. Mathar, Apr 16 2016
  • Mathematica
    A271487T[n_] := A271487T[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = A271487T[Floor[n/2]]; If[EvenQ[n], {an[[3]], an[[1]] + an[[3]], an[[2]]}, {an[[1]], an[[2]], an[[1]] + an[[3]]}]]];
a[n_] := a[n] = Module[{a = 0, l, nMax}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, nMax = Max[A271487T[l]]; a = Max[a, nMax]]; a];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 20}] (* Jean-François Alcover, Nov 17 2017, after R. J. Mathar *)

Formula

Conjectures from Lars Blomberg, Jan 08 2018: (Start)
n mod 3 == 0: a(n)=a(n-1)+a(n-4) for n>5.
n mod 3 == 1: a(n)=a(n-1)+a(n-4)-a(n-10) for n>9.
n mod 3 == 2: a(n)=a(n-1)+a(n-4)-a(n-14)-a(n-21) for n>22.
(End)
Conjectures from Colin Barker, Jan 09 2018: (Start)
G.f.: (1 + 2*x + 3*x^2 + 2*x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^10 - x^13) / (1 - 2*x^3 - x^6 - x^9).
a(n) = 2*a(n-3) + a(n-6) + a(n-9) for n>8.
(End)

Extensions

a(11)-a(20) b R. J. Mathar, Apr 16 2016
a(21)-a(40) from Lars Blomberg, Jan 08 2018
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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