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.

User: Gianmarco Giordano

Gianmarco Giordano's wiki page.

Gianmarco Giordano has authored 8 sequences.

A263045 a(1)=a(2)=1, a(3)=2; for n>3, a(n) = (a(n-1) + a(n-2))*a(n-3) - a(n-1).

Original entry on oeis.org

1, 1, 2, 1, 2, 4, 2, 10, 38, 58, 902, 35578, 2080262, 1906407418, 67898268271622, 141250085279900836858, 269280339671247778784817867782, 18283668752862244903904463537467802693858298, 2582569770571288306580588933602503511656010789600193877369998342
Offset: 1

Views

Author

Gianmarco Giordano, Oct 08 2015

Keywords

Programs

  • Magma
    I:=[1,1,2]; [n le 3 select I[n]  else (Self(n-1)+ Self(n-2))*Self(n-3)-Self(n-1): n in [1..20]]; // Vincenzo Librandi, Oct 09 2015
  • Mathematica
    RecurrenceTable[{a[1]==a[2]==1,a[3]==2,a[n]==(a[n-1]+a[n-2])a[n-3]-a[n-1]}, a,{n,20}] (* Harvey P. Dale, Jul 23 2018 *)
  • PARI
    a(n) = if(n<4, fibonacci(n), (a(n-1)+a(n-2))*a(n-3)-a(n-1)) \\ Altug Alkan, Oct 08 2015

Extensions

More terms from Altug Alkan, Oct 08 2015

A258588 Minimal most likely sum for a roll of n 10-sided dice.

Original entry on oeis.org

1, 11, 16, 22, 27, 33, 38, 44, 49, 55, 60, 66, 71, 77, 82, 88, 93, 99, 104, 110, 115, 121, 126, 132, 137, 143, 148, 154, 159, 165, 170, 176, 181, 187, 192, 198, 203, 209, 214, 220, 225, 231, 236, 242, 247, 253, 258, 264, 269, 275
Offset: 1

Views

Author

Gianmarco Giordano, Nov 06 2015

Keywords

Examples

			For n=1, there are ten equally likely outcomes, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and the smallest of these is 1, so a(1)=1.

Links

Crossrefs

Cf. A030123, A256680, A263941.

Programs

  • Mathematica
    Join[{1}, Table[(22 n + (-1)^n - 1)/4, {n, 2, 50}]]
  • PARI
    a(n)=if(n<2, 1,11*n\2);
vector(50, n, a(n))

Formula

G.f.: x*(1 + 10*x + 4*x^2 - 4*x^3)/((1 - x)^2*(1 + x)).
a(n) = floor(11*n/2) = (22*n + (-1)^n - 1)/4 with n>1, a(1)=1.
a(n) = a(n-1) + a(n-2) - a(n-3) for n>4.

A258589 Minimal most likely sum for a roll of n 12-sided dice.

Original entry on oeis.org

1, 13, 19, 26, 32, 39, 45, 52, 58, 65, 71, 78, 84, 91, 97, 104, 110, 117, 123, 130, 136, 143, 149, 156, 162, 169, 175, 182, 188, 195, 201, 208, 214, 221, 227, 234, 240, 247, 253, 260, 266, 273, 279, 286, 292, 299, 305, 312, 318, 325, 331, 338, 344, 351, 357
Offset: 1

Views

Author

Gianmarco Giordano, Nov 06 2015

Keywords

Examples

			For n=1, there are twelve equally likely outcomes, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and the smallest of these is 1, so a(1)=1.

Links

Crossrefs

Cf. A030123, A256680, A263941, A258588.

Programs

  • Mathematica
    Join[{1}, Table[(26 n + (-1)^n - 1)/4, {n, 2, 50}]]
  • PARI
    a(n)=if(n<2, 1, 13*n\2);
vector(50, n, a(n))
  • PARI
    a(n) = if(n<2,n, (26*n + (-1)^n - 1)/4);
vector(50, n, a(n))
  • PARI
    Vec(-x*(5*x^3-5*x^2-12*x-1)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Nov 06 2015

Formula

a(n) = floor(13*n/2) = (26*n + (-1)^n - 1)/4 with n>1, a(1)=1.
a(n) = a(n-1) + a(n-2) - a(n-3) for n>4.
G.f.: -x*(5*x^3-5*x^2-12*x-1) / ((x-1)^2*(x+1)). - Colin Barker, Nov 06 2015

A263941 Minimal most likely sum for a roll of n 8-sided dice.

Original entry on oeis.org

1, 9, 13, 18, 22, 27, 31, 36, 40, 45, 49, 54, 58, 63, 67, 72, 76, 81, 85, 90, 94, 99, 103, 108, 112, 117, 121, 126, 130, 135, 139, 144, 148, 153, 157, 162, 166, 171, 175, 180, 184, 189, 193, 198, 202, 207, 211, 216, 220, 225
Offset: 1

Views

Author

Gianmarco Giordano, Oct 30 2015

Keywords

Examples

			For n=1, there are eight equally likely outcomes, 1,2,3,4,5,6,7,8 and the smallest of these is 1, so a(1)=1.

Links

Crossrefs

Cf. A030123, A130877, A256680.

Programs

  • Mathematica
    Join[{1}, Table[(18 n + (-1)^n - 1)/4, {n, 2, 50}]]
  • PARI
    a(n)=if(n<2,1,9*n\2);
vector(50,n,a(n))

Formula

G.f.: x*(1 + 8*x + 3*x^2 - 3*x^3)/((1 - x)^2*(1 + x)).
a(n) = floor(9*n/2) = (18*n + (-1)^n - 1)/4 with n>1, a(1)=1.
a(n) = a(n-1) + a(n-2) - a(n-3) for n>4.
a(n) = -A130877(-n+1) for n>1.

Extensions

Edited by Bruno Berselli, Oct 30 2015

A263048 a(0)=0, a(1)=1; for n>1, a(n) = a(n-2)^a(n-1) + a(n-1)^a(n-2).

Original entry on oeis.org

0, 1, 1, 2, 3, 17, 129145076
Offset: 0

Views

Author

Gianmarco Giordano, Oct 08 2015

Keywords

Comments

Next term has 365895553 digits.

Programs

  • Magma
    [n le 2 select n-1 else Self(n-2)^Self(n-1)+Self(n-1)^Self(n-2): n in [1..7]]; // Vincenzo Librandi, Oct 09 2015
  • Mathematica
    RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == a[n-2]^a[n-1]+a[n-1]^a[n-2]}, a, {n, 6}] (* Vincenzo Librandi, Oct 09 2015 *)
nxt[{a_,b_}]:={b,a^b+b^a}; NestList[nxt,{0,1},6][[;;,1]] (* Harvey P. Dale, May 02 2023 *)
  • PARI
    a(n) = if(n<2, n, a(n-2)^a(n-1)+a(n-1)^a(n-2)) \\ Altug Alkan, Oct 15 2015

A263044 a(1) = a(2) = a(3) = 1; for n>3, a(n) = (a(n-3) + a(n-1))*(a(n-2) + a(n-3)).

Original entry on oeis.org

1, 1, 1, 4, 10, 55, 826, 54340, 47921995, 2643710343286, 126835535679488180710, 335322495784116748418182251685105, 42530809264656915340847577048392358554130713446770436
Offset: 1

Views

Author

Gianmarco Giordano, Oct 08 2015

Keywords

Programs

  • Magma
    [n le 3 select 1  else (Self(n-3)+ Self(n-1))*(Self(n-2)+Self(n-3)): n in [1..15]]; // Vincenzo Librandi, Oct 09 2015
  • Mathematica
    RecurrenceTable[{a[1] == a[2] == a[3] == 1, a[n] == (a[n - 3] + a[n - 1]) (a[n - 2] + a[n - 3])}, a, {n, 15}] (* Bruno Berselli, Oct 09 2015 *)
  • PARI
    a(n) = if(n<4, 1, (a(n-3)+a(n-1))*(a(n-2)+a(n-3)));
vector(15, n, a(n)) \\ Altug Alkan, Oct 08 2015

Formula

a(n) = (a(n-3) + a(n-1))*(a(n-2) + a(n-3)) for n>=4; a(1)=a(2)=a(3)=1.

Extensions

More terms from Altug Alkan, Oct 08 2015

A263047 a(1)=0, a(2)=1, a(3)=2; for n>3, a(n) = a(n-3)*a(n-1) - a(n-2).

Original entry on oeis.org

0, 1, 2, -1, -3, -5, 8, -19, 87, 715, -13672, -1190179, -850964313, 11634385277515, -13847001034356560872, 11783303722311508585098883421, 137091495347348713307137824784782074139687, -1898306077876225285447341619480271058010077969630158545410485
Offset: 1

Views

Author

Gianmarco Giordano, Oct 08 2015

Keywords

Programs

  • Magma
    [n le 3 select n-1 else Self(n-3)*Self(n-1)-Self(n-2): n in [1..20]]; // Vincenzo Librandi, Oct 09 2015
  • Maple
    a[1]:= 0: a[2]:= 1: a[3]:= 2:
for n from 4 to 20 do
  a[n]:= a[n-3]*a[n-1]-a[n-2]
od:
seq(a[i],i=1..20); # Robert Israel, Oct 08 2015
  • Mathematica
    nxt[{a_,b_,c_}]:={b,c,a*c-b}; NestList[nxt,{0,1,2},20][[All,1]] (* Harvey P. Dale, Feb 02 2022 *)
  • PARI
    a(n) = if(n<4, n-1, a(n-3)*a(n-1)-a(n-2));
vector(20, n, a(n)) \\ Altug Alkan, Oct 08 2015

A263043 a(n)=n for n = 1..5; for n>=6, a(n) = a(n-5)*a(n-3)*a(n-1) - a(n-4)*a(n-2).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 41, 587, 16231, 3323246, 13654552343, 9086706651503151, 17725851219520961162682469, 3928527920941441960398255684700870518131, 118631177920294161985904111240557003105520588984802122222460259
Offset: 1

Views

Author

Gianmarco Giordano, Oct 08 2015

Keywords

Programs

  • Magma
    [n le 5 select n else Self(n-5)*Self(n-3)*Self(n-1)-Self(n-4)*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Oct 09 2015
  • Mathematica
    nxt[{a_,b_,c_,d_,e_}]:={b,c,d,e,a*c*e-b*d}; NestList[nxt,{1,2,3,4,5},15][[;;,1]] (* Harvey P. Dale, Dec 21 2024 *)
  • PARI
    a(n) = if(n<6, n, a(n-5)*a(n-3)*a(n-1)-a(n-4)*a(n-2));
vector(20, n, a(n)) \\ Altug Alkan, Oct 08 2015

Extensions

More terms from Altug Alkan, Oct 08 2015

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