A132839 -id:A132839 - cp's OEIS frontend

A132840 Largest integer terms forming a self-convolution fifth-root of a sequence (A132839) such that: A132839(n) <= 5*A132839(n-1) for n>0 with A132839(0)=1.

1, 1, 3, 11, 44, 184, 800, 3544, 15950, 72666, 334276, 1549876, 7232910, 33939590, 160002964, 757355152, 3597467523, 17140996739, 81896369733, 392242556233, 1882772831063, 9055276934011, 43630125033845, 210563441647421

Offset: 0

Paul D. Hanna, Sep 10 2007

nonn

Cf. A132839 (fifth power).

A132855 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 5th power of an integer sequence such that 0 < c(n) <= 5*c(n-1) for n>0 with c(0)=1.

Original entry on oeis.org

1, 1, 5, 75, 3625, 638750, 442823125, 1278820631250, 15775429658296875, 848938273203627578125, 202483260558673741179296875, 216741216953142470752123517187500, 1051774892873652266440974611041742187500

Offset: 0

Paul D. Hanna, Sep 19 2007, Oct 06 2007

nonn

The minimal path in the 5-convoluted tree is A083955 and the maximal path is A132839.

Equals the number of nodes at generation n in the 5-convoluted tree, which is defined as follows: tree of all finite sequences {c(k), k=0..n} that form the initial terms of a self-convolution 5th power of some integer sequence such that 0 < c(n) <= 5*c(n-1) for n>0 with a(0)=1.

			a(n) counts the nodes in generation n of the following tree.
Generations 0..3 of the 5-convoluted tree are as follows;
The path from the root is shown, with child nodes enclosed in [].
GEN.0: [1];
GEN.1: 1->[5];
GEN.2: 1-5->[5,10,15,20,25];
GEN.3:
1-5-5->[5,10,15,20,25]
1-5-10->[5,10,15,20,25,30,35,40,45,50]
1-5-15->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75]
1-5-20->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100]
1-5-25->[5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105, 110,115,120,125].
Each path in the tree from the root node forms the initial terms of a self-convolution 5th power of a sequence of integer terms.

Martin Fuller, Computing A132852, A132853, A132854, A132855, A132856

Cf. A132852, A132853, A132854, A132856; A083955, A132839.

Extended by Martin Fuller, Sep 24 2007

A132837 Largest terms a(n) forming a self-convolution 4th power of an integer sequence (A132838) such that: a(n) <= 4*a(n-1) for n>0 with a(0)=1.

Original entry on oeis.org

1, 4, 14, 56, 221, 884, 3534, 14136, 56542, 226168, 904672, 3618688, 14474751, 57899004, 231596014, 926384056, 3705536222, 14822144888, 59288579552, 237154318208, 948617272832, 3794469091328, 15177876365312, 60711505461248

Offset: 0

Paul D. Hanna, Sep 10 2007

nonn

Cf. A132838 (fourth-root); variants: A132831, A132835, A132839.

{a(n)=local(A,t,r=1);A=if(n==0,[1],vector(n,j,a(j-1)));if(n==0,r=1,t=a(n-1); if(denominator(Vec(Ser(concat(A,4*t))^(1/4))[n+1])==1,r=4*t, if(denominator(Vec(Ser(concat(A,4*t-1))^(1/4))[n+1])==1,r=4*t-1, if(denominator(Vec(Ser(concat(A,4*t-2))^(1/4))[n+1])==1,r=4*t-2,r=4*t-3))));r}

cp's OEIS Frontend

A132840 Largest integer terms forming a self-convolution fifth-root of a sequence (A132839) such that: A132839(n) <= 5*A132839(n-1) for n>0 with A132839(0)=1.

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A132855 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 5th power of an integer sequence such that 0 < c(n) <= 5*c(n-1) for n>0 with c(0)=1.

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A132837 Largest terms a(n) forming a self-convolution 4th power of an integer sequence (A132838) such that: a(n) <= 4*a(n-1) for n>0 with a(0)=1.

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