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
a(4) = a(1)*a(2)*a(3) - (a(1) + a(2) + a(3)) = 2*5*3 - (2 + 5 + 3) = 20.
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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}]
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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
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
a(3) = a(1) * a(2) - (a(1) + a(2)) = 2 * 5 - (2 + 5) = 3.
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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
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RecurrenceTable[{x[n+1]==x[n]*x[n-1]-(x[n]+x[n-1]),x[1]==2,x[2]==5},x,{n,1,18}]
A276972
a(n) = n^(2*(2*n^4+1)).
Original entry on oeis.org
0, 1, 73786976294838206464
Offset: 0
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
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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;}
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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
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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 *)
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
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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;}
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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 *)
A276274
a(n) = (2*n+1)^(2*(2*n+1)^2).
Original entry on oeis.org
1, 387420489, 88817841970012523233890533447265625, 66009724686219550843768321818371771650147004059278069406814190436565131829325062449
Offset: 0
For n = 1, k = 3^2 = 9 and so a(1) = 3^(2*3^2) = 3^18 = 387420489.
Subsequence of
A000312, containing only the odd squares.
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