A165896
a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)+a(n-1)*a(n-3)+a(n-2)*a(n-3))/a(n-4) with four initial ones.
Original entry on oeis.org
1, 1, 1, 1, 6, 51, 3001, 9180001, 14050074147451, 3870680638643416483474006, 4992392071450646411005278674572370014340582601, 2715030052293379508289500941366397276374058263752394148988972928520177978202810359001
Offset: 0
- Seiichi Manyama, Table of n, a(n) for n = 0..15
- S. Fomin, A. Zelevinsky, The Laurent Phenomenon, Adv. Appl. Math. 28 (2) (2002) 119-144. [_R. J. Mathar_, Oct 23 2009]
- Sergey Fomin, Andrei Zelevinsky, The Laurent phenomenon, arXiv:math/0104241 [math.CO], 2001. [_R. J. Mathar_, Oct 23 2009]
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RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1,a[n]==(a[n-1]^2+a[n-2]^2+a[n-3]^2+ a[n-1]a[n-2]+ a[n-1]a[n-3]+a[n-2]a[n-3])/a[n-4]},a,{n,13}] (* Harvey P. Dale, May 21 2012 *)
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a(n)=if(n<4,1,(a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-1)*a(n-2)+a(n-1)*a(n-3)+a(n-2)*a(n-3))/a(n-4))
A276122
a(0) = a(1) = a(2) = 1; for n > 2, a(n) = (a(n-1)^2+a(n-2)^2+a(n-1)+a(n-2))/a(n-3).
Original entry on oeis.org
1, 1, 1, 4, 22, 526, 69427, 219111589, 91273561736491, 119994570874632853695766, 65713991236617279734602790963627271046, 47311933073383646516067037755547920981262829886906923065810924
Offset: 0
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RecurrenceTable[{a[n] == (a[n - 1]^2 + a[n - 2]^2 + a[n - 1] + a[n - 2])/a[n - 3], a[0] == a[1] == a[2] == 1}, a, {n, 0, 11}] (* Michael De Vlieger, Aug 21 2016 *)
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).
Original entry on oeis.org
1, 1, 1, 1, 4, 22, 589, 399253, 41144206447, 77387327118194895379, 10169897514576967837097322386922878932, 259050897146323086186965020577200627526185475088368701480903471601830
Offset: 0
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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
A276126
a(0) = a(1) = a(2) = a(3) = a(4) = 1; for n>4, a(n) = ( a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-4)^2+a(n-1)*a(n-2)*a(n-3)*a(n-4) ) / a(n-5).
Original entry on oeis.org
1, 1, 1, 1, 1, 5, 33, 1281, 1853441, 3826997739521, 2989151785658720873470945, 271581474754155314350055167823358355425497243141, 57581776430597685625970981157448022010386123824977761496513036956000541901241585948341716033
Offset: 0
-
nxt[{a_,b_,c_,d_,e_}]:={b,c,d,e,(e^2+d^2+c^2+b^2+e*d*c*b)/a}; NestList[nxt,{1,1,1,1,1},15][[All,1]] (* Harvey P. Dale, Aug 08 2022 *)
-
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 A276126(n)
A(5, n)
end
A276131
a(n) = (a(n-1)^2+a(n-2)^2+a(n-3)^2+a(n-4)^2+a(n-1)*a(n-2)+a(n-1)*a(n-3)+a(n-1)*a(n-4)+a(n-2)*a(n-3)+a(n-2)*a(n-4)+a(n-3)*a(n-4))/a(n-5) with five initial ones.
Original entry on oeis.org
1, 1, 1, 1, 1, 10, 136, 20251, 413100001, 170660037240000001, 2912484838126132813026335712191641, 62371823031725048177115183368983888882661870237372850050710016335
Offset: 0
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nxt[{a_,b_,c_,d_,e_}]:={b,c,d,e,15(b*c*d*e)-a-b-c-d-e}; NestList[nxt,{1,1,1,1,1},15][[;;,1]] (* Harvey P. Dale, May 18 2024 *)
Showing 1-5 of 5 results.