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: Christopher C. Capobianco

Christopher C. Capobianco's wiki page.

Christopher C. Capobianco has authored 6 sequences.

A309080 Product minus sum of all previous terms in the sequence, starting with a(1) = 2 and a(2) = 5.

Original entry on oeis.org

2, 5, 3, 20, 570, 341400, 116758458000, 13632577445813641200000, 185847167817698504752014113195034069600000000, 34539169785859790805229099212216829464451540660176789302662465332580254227520000000000000
Offset: 1

Author

Keywords

Examples

			a(4) = a(1)*a(2)*a(3) - (a(1) + a(2) + a(3)) = 2*5*3 - (2 + 5 + 3) = 20.
		

Crossrefs

Cf. A123702.

Programs

  • Mathematica
    x1 = 2; x2 = 5; p = x1 * x2; s = x1 + x2; x = p - s; A309080 = {x1, x2, x}; Do[p = p * x; s = s + x; x = p - s; AppendTo[A309080, x], {n, 16}]
  • Python
    a, n, p, s = [2,5], 2, 2, 2
    while n < 10:
        p, s, n = p*a[len(a)-1], s+a[len(a)-1], n+1
        a = a+[p-s]
    for n in range(1, 11): print(a[n-1], end=', ') # A.H.M. Smeets, Aug 22 2019

Formula

a(n) = Product_{k=1..n-1} a(k) - Sum_{k=1..n-1} a(k) with a(1) = 2, a(2) = 5.

A309006 Product minus sum of the two previous terms in the sequence, with a(1) = 2 and a(2) = 5.

Original entry on oeis.org

2, 5, 3, 7, 11, 59, 579, 33523, 19375715, 649512684707, 12584772018235630083, 8173969059977170083865314925891, 102867537103924486790122812065087346778963284622979
Offset: 1

Author

Keywords

Examples

			a(3) = a(1) * a(2) - (a(1) + a(2)) = 2 * 5 - (2 + 5) = 3.
		

Crossrefs

Programs

  • Magma
    I:=[2,5]; [n le 2 select I[n] else Self(n-1)*Self(n-2)-(Self(n-1)+Self(n-2)): n in [1..14]]; // Vincenzo Librandi, Jul 10 2019
  • Mathematica
    RecurrenceTable[{x[n+1]==x[n]*x[n-1]-(x[n]+x[n-1]),x[1]==2,x[2]==5},x,{n,1,18}]

Formula

a(n) = a(n-1)*a(n-2) - (a(n-1)+a(n-2)), with a(1) = 2, a(2) = 5.

A276972 a(n) = n^(2*(2*n^4+1)).

Original entry on oeis.org

0, 1, 73786976294838206464
Offset: 0

Author

Keywords

Comments

a(3) has 156 decimal digits. - Tyler Busby, Jan 30 2023

Crossrefs

Programs

  • Mathematica
    Table[k^(2*(2*k^4+1)),{k,0,9}]

A275825 Third-order sequence with non-constant coefficients: a(n) = (n-3)*a(n-1) + (n-1)*a(n-3); a(0) = a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 1, 2, 5, 14, 52, 238, 1288, 8144, 59150, 486080, 4464304, 45352840, 505200280, 6124903616, 80304039608, 1132339758992, 17089219746352, 274872988654576, 4694355262548640, 84840179120802560, 1617735736056994736, 32457990536915964800, 683569125395013719680
Offset: 0

Author

Keywords

Crossrefs

Programs

  • C
    int seq(int n) {int v = 1; if(n <= 2) {v = 1;} else {v = (n-3)*seq(n-1) + (n-1)*seq(n-3);}return v;}
  • Maple
    f:= gfun:-rectoproc({a(n) = (n-3)*a(n-1) + (n-1)*a(n-3), a(0) = 1,a(1) = 1, a(2) = 1}, a(n), remember):
    map(f, [$0..30]); # Robert Israel, Nov 08 2016
  • Mathematica
    RecurrenceTable[{a[n+1]==(n-2)*a[n]+n*a[n-2],a[0]==1,a[1]==1,a[2]==1},a,{n,0,15}]
    nxt[{n_,a_,b_,c_}]:={n+1,b,c,c(n-2)+n*a}; NestList[nxt,{2,1,1,1},30][[;;,2]] (* Harvey P. Dale, Jul 22 2025 *)

Formula

a(n) ~ c * n^(n-5/2) / exp(n), where c = 35.33624296996624315241349866820530476... . - Vaclav Kotesovec, Oct 04 2016

A276693 a(n) = a(n-2)*a(n-3) - a(n-1); a(0) = 3, a(1) = 5, a(2) = 7.

Original entry on oeis.org

3, 5, 7, 8, 27, 29, 187, 596, 4827, 106625, 2770267, 511908608, 294867810267, 1417828655948069, 150943952469132130267, 418071880169258361764894156, 214012660834726939177944668730210267, 63105422008735225121538219609433904551328809385
Offset: 0

Author

Keywords

Programs

  • C
    int seq(int n) {int v = 3; if(n <= 2) {v = 3+2*n;} else {v = seq(n-2)*seq(n-3) - seq(n-1);} return v;}
  • Mathematica
    RecurrenceTable[{a[n] ==  a[n-2]*a[n-3]-a[n-1], a[0] == 3,a[1]==5,a[2]==7}, a, {n,0, 17}]
    nxt[{a_,b_,c_}]:={b,c,a*b-c}; NestList[nxt,{3,5,7},20][[All,1]] (* Harvey P. Dale, May 27 2020 *)

Formula

a(n) ~ c^(d^n), where c = 2.46982021132238000769..., d = A060006 = (1/2+sqrt(23/108))^(1/3) + (1/2-sqrt(23/108))^(1/3) = 1.32471795724474602596..., real root of the equation d*(d^2-1) = 1. - Vaclav Kotesovec, Oct 04 2016

A276274 a(n) = (2*n+1)^(2*(2*n+1)^2).

Original entry on oeis.org

1, 387420489, 88817841970012523233890533447265625, 66009724686219550843768321818371771650147004059278069406814190436565131829325062449
Offset: 0

Author

Keywords

Comments

All terms are odd squares and are of the form k^k, where k = (2n+1)^2.

Examples

			For n = 1, k = 3^2 = 9 and so a(1) = 3^(2*3^2) = 3^18 = 387420489.
		

Crossrefs

Subsequence of A000312, containing only the odd squares.
Intersection of A000312 and A016754.

Programs