A072878 -id:A072878 - cp's OEIS frontend

A276124 a(0) = a(1) = a(2) = a(3) = 1; for n > 3, a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)a(n-2)a(n-3))/a(n-4).

1, 1, 1, 1, 4, 22, 589, 399253, 41144206447, 77387327118194895379, 10169897514576967837097322386922878932, 259050897146323086186965020577200627526185475088368701480903471601830

Offset: 0

Bruno Langlois, Aug 21 2016

nonn

Seiichi Manyama, Table of n, a(n) for n = 0..15

Cf. A165903, A072878.

RecurrenceTable[{a[n] == (a[n - 1]^2 + a[n - 2]^2 + a[n - 3]^2 + a[n - 1] a[n - 2] a[n - 3])/a[n - 4], a[0] == a[1] == a[2] == a[3] == 1}, a, {n, 0, 11}] (* Michael De Vlieger, Aug 21 2016 *)

def A(m, n)
  a = Array.new(m, 1)
  ary = [1]
  while ary.size < n + 1
    i = a[1..-1].inject(0){|s, i| s + i * i} + a[1..-1].inject(:*)
    break if i % a[0] > 0
    a = *a[1..-1], i / a[0]
    ary << a[0]
  end
  ary
end
def A276124(n)
  A(4, n)
end # Seiichi Manyama, Aug 21 2016

a(n) = 8*a(n-1)*a(n-2)*a(n-3)-a(n-1)*a(n-2)-a(n-1)*a(n-3)-a(n-2)*a(n-3)-a(n-4).

A113848 a(1) = a(2) = 1, a(n+2) = 2*a(n) + a(n+1)^2.

Original entry on oeis.org

1, 1, 3, 11, 127, 16151, 260855055, 68045359719085327, 4630170979299719971778494028407039, 21438483297549327871400796194793048411084076762817293736211302918175

Offset: 1

Jonathan Vos Post, Jan 24 2006

In this sequence the primes begin a(3) = 3, a(4) = 11, a(5) = 127, a(9) = 4630170979299719971778494028407039.

			a(1) = 1 by definition.
a(2) = 1 by definition.
a(3) = 2*1 + 1^2 = 3.
a(4) = 2*1 + 3^2 = 11.
a(5) = 2*3 + 11^2 = 127.
a(6) = 2*11 + 127^2 = 16151.

Index entries for sequences of form a(n+1)=a(n)^2 + ...

Cf. A000278, A000283, A014253, A063827, A072878, A112957, A112958, A112959, A112960, A112961, A112969, A113785.

Join[{a=1,b=1},Table[c=1*b^2+2*a;a=b;b=c,{n,10}]] (* Vladimir Joseph Stephan Orlovsky, Jan 18 2011 *)
RecurrenceTable[{a[1]==1, a[2]==1, a[n] == 2*a[n-2] + a[n-1]^2}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)

a(1) = a(2) = 1, for n>2: a(n) = 2*a(n-2) + a(n-1)^2. a(1) = a(2) = 1, for n>0: a(n+2) = 2*a(n) + a(n+1)^2.

a(n) ~ c^(2^n), where c = 1.163464453662702696843453679269882816346479873363677551158525103156732040997... . - Vaclav Kotesovec, Dec 18 2014

A113592 Array of quadratic pseudofibonacci sequences, read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 1, 3, 6, 11, 1, 4, 11, 40, 127, 1, 5, 18, 127, 1612, 16151, 1, 6, 27, 332, 16151, 2598264, 260855055, 1, 7, 38, 739, 110260

Offset: 1

Jonathan Vos Post, Jan 26 2006

Row 1 is A113848. Column 1 is A000012 (the simplest sequence of positive numbers: the all 1's sequence). Column 2 is A000027 (the natural numbers) = n. Column 3 is A010000 = A059100(n+1) = n^2 + 2. Column 4 is 2*n + (n^2 + 2)^2 = n^4 + 4*n^2 + 2*n + 4. Column 5 is 2*(n^2 + 2) + (n^4 + 4*n^2 + 2*n + 4)^2 = n^8 + 8*n^6 + 4*n^5 + 24*n^4 + 16*n^3 + 38*n^2 + 16*n + 20.

			Table (upper left corner):
1...1...3...11...127....16151...260855055...
1...2...6...40...1612...2598624.675284696600...
1...3...11..127..16151..260855055...
1...4...18..332..110260.12157268264...
1...5...27..739..546175...
1...6...38..1456.2120012...
1...7...51..2615.6838327...
1...8...66..4372.19114516...
1...9...83..6907.47706815
1..10..102..10424.108659980...

Cf. A000012, A000027, A000278, A000283, A010000, A014253, A059100, A063827, A072878, A112957, A112958, A112959, A112960, A112961, A112969, A113785.

Antidiagonals of table: T(i, j) = j-th iteration of a(i, 0) = 1, a(i, 1) = i and for j>1: a(i, j) = 2*a(i, j-2) + a(i, j-1)^2.

cp's OEIS Frontend

A276124 a(0) = a(1) = a(2) = a(3) = 1; for n > 3, a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)a(n-2)a(n-3))/a(n-4).

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A113848 a(1) = a(2) = 1, a(n+2) = 2*a(n) + a(n+1)^2.

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A113592 Array of quadratic pseudofibonacci sequences, read by antidiagonals.

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Author

Keywords

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Examples

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Formula

cp's OEIS Frontend

A276124 a(0) = a(1) = a(2) = a(3) = 1; for n > 3, a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)*a(n-3))/a(n-4).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Ruby

Formula

A113848 a(1) = a(2) = 1, a(n+2) = 2*a(n) + a(n+1)^2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A113592 Array of quadratic pseudofibonacci sequences, read by antidiagonals.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A276124 a(0) = a(1) = a(2) = a(3) = 1; for n > 3, a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)a(n-2)a(n-3))/a(n-4).