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.

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

A271488 Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,23,e).

Original entry on oeis.org

1, 2, 3, 4, 5, 8, 11, 15, 21, 30, 41, 56, 79, 112, 153, 209, 297, 418, 571, 782, 1109, 1560, 2131, 2940, 4141, 5822, 7953, 10981, 15455, 21728, 29681, 41003, 57681, 81090, 110771, 153105, 215269, 302632, 413403, 571428, 803397
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
    A271488T := 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(2,an),op(1,an)+op(3,an),op(3,an)] ;
        else
            # apply F1
            [op(1,an),op(2,an),op(1,an)+op(3,an)] ;
        end if;
    end if;
end proc:
A271488 := proc(n)
    local a,l,nmax;
    a := 0 ;
    for l from 2^n to 2^(n+1)-1 do
        nmax := max( op(A271488T(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[[2]], an[[1]] + an[[3]], an[[3]]}, {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 *)

Extensions

a(4) corrected by Jean-François Alcover and Vaclav Kotesovec, Nov 18 2017
a(21)-a(24) from Vaclav Kotesovec, Nov 18 2017
a(25)-a(26) from Vaclav Kotesovec, Nov 29 2017
a(27)-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

A271893 Expansion of (2*x+1)*(1-x) / ( 1-2*x-4*x^2+6*x^3 ).

Original entry on oeis.org

1, 3, 8, 22, 58, 156, 412, 1100, 2912, 7752, 20552, 54640, 144976, 385200, 1022464, 2715872, 7210400, 19149504, 50845376, 135026368, 358537216, 952107648, 2528205952, 6713619200, 17827416320, 47340073728, 125708097536, 333811992064, 886415931904, 2353831246848, 6250454268928, 16597737933824
Offset: 0

Views

Author

R. J. Mathar, Apr 16 2016

Keywords

Comments

Sum of all first elements at level n of the TRIP-Stern sequence corresponding to the permutation triple (e,13,23)

Links

Crossrefs

Cf. A271486 (maximum at level n).

Programs

  • PARI
    x='x+O('x^99); Vec((2*x+1)*(1-x)/(1-2*x-4*x^2+6*x^3)) \\ Altug Alkan, Apr 16 2016

Formula

a(n) >= 2^n.

A271894 Expansion of (1+x-3*x^2) / ( 1-2*x-4*x^2+6*x^3 ).

Original entry on oeis.org

1, 3, 7, 20, 50, 138, 356, 964, 2524, 6768, 17848, 47624, 126032, 335472, 889328, 2364352, 6273184, 16667808, 44242240, 117516608, 311995328, 828603648, 2200088960, 5842620544, 15513975040, 41197898496, 109395973888, 290499691520, 771395887616
Offset: 0

Views

Author

R. J. Mathar, Apr 16 2016

Keywords

Comments

Sum of all second elements at level n of the TRIP-Stern sequence corresponding to the permutation triple (e,13,23)

Links

Crossrefs

Cf. A271486 (maximum at level n).

Programs

  • Mathematica
    CoefficientList[Series[(1+x-3x^2)/(1-2x-4x^2+6x^3),{x,0,30}],x] (* or *) LinearRecurrence[{2,4,-6},{1,3,7},30] (* Harvey P. Dale, Jul 14 2024 *)
  • PARI
    x='x+O('x^99); Vec((1+x-3*x^2)/(1-2*x-4*x^2+6*x^3)) \\ Altug Alkan, Apr 16 2016

Formula

a(n) >= 2^n.

A271895 Expansion of (1-2*x^2) / ( 1-2*x-4*x^2+6*x^3 ).

Original entry on oeis.org

1, 2, 6, 14, 40, 100, 276, 712, 1928, 5048, 13536, 35696, 95248, 252064, 670944, 1778656, 4728704, 12546368, 33335616, 88484480, 235033216, 623990656, 1657207296, 4400177920, 11685241088, 31027950080, 82395796992, 218791947776, 580999383040, 1542791775232
Offset: 0

Views

Author

R. J. Mathar, Apr 16 2016

Keywords

Comments

Sum of all third elements at level n of the TRIP-Stern sequence corresponding to the permutation triple (e,13,23)

Links

Crossrefs

Cf. A271486 (maximum at level n).

Programs

  • PARI
    x='x+O('x^99); Vec((1-2*x^2)/(1-2*x-4*x^2+6*x^3)) \\ Altug Alkan, Apr 16 2016

Formula

a(n) >= 2^n.
Showing 1-7 of 7 results.

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

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