A132837 -id:A132837 - cp's OEIS frontend

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

1, 1, 2, 7, 22, 78, 273, 984, 3573, 13138, 48670, 181625, 681630, 2570979, 9738171, 37021873, 141199583, 540058408, 2070814185, 7958280782, 30646175351, 118230058466, 456879024997, 1768206394844, 6852795439360, 26592367534410

Offset: 0

Paul D. Hanna, Sep 10 2007

nonn

Cf. A132837 (fourth power).

A132854 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 4th power of an integer sequence such that 0 < c(n) <= 4*c(n-1) for n>0 with c(0)=1.

Original entry on oeis.org

1, 1, 4, 32, 736, 47600, 9901728, 6780161344, 15819971230848, 128391245362464512, 3685238521747987153664, 378871127417706380405937152, 140962622184196263047081802452992, 191428155805533938524028481989647915008

Offset: 0

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

nonn

The minimal path in the 4-convoluted tree is A083954 and the maximal path is A132837.

Equals the number of nodes at generation n in the 4-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 4th power of some integer sequence such that 0 < c(n) <= 4*c(n-1) for n>0 with a(0)=1. - Paul D. Hanna, Oct 06 2007

			a(n) counts the nodes in generation n of the following tree.
Generations 0..3 of the 4-convoluted tree are as follows;
The path from the root is shown, with child nodes enclosed in [].
GEN.0: [1];
GEN.1: 1->[4];
GEN.2: 1-4->[2,6,10,14];
GEN.3:
1-4-2->[4,8]
1-4-6->[4,8,12,16,20,24]
1-4-10->[4,8,12,16,20,24,28,32,36,40]
1-4-14->[4,8,12,16,20,24,28,32,36,40,44,48,52,56].
Each path in the tree from the root node forms the initial terms of a self-convolution 4th power of a sequence of integer terms.

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

Cf. A132852, A132853, A132855, A132856; A083954, A132837.

Extended by Martin Fuller, Sep 24 2007

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

Original entry on oeis.org

1, 5, 25, 125, 625, 3121, 15605, 78025, 390125, 1950625, 9753123, 48765615, 243828075, 1219140375, 6095701875, 30478509371, 152392546855, 761962734275, 3809813671375, 19049068356875, 95245341784374, 476226708921870

Offset: 0

Paul D. Hanna, Sep 10 2007

nonn

Cf. A132840 (fifth-root); variants: A132831, A132835, A132837.

{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,5*t))^(1/5))[n+1])==1,r=5*t, if(denominator(Vec(Ser(concat(A,5*t-1))^(1/5))[n+1])==1,r=5*t-1, if(denominator(Vec(Ser(concat(A,5*t-2))^(1/5))[n+1])==1,r=5*t-2, if(denominator(Vec(Ser(concat(A,5*t-3))^(1/5))[n+1])==1,r=5*t-3,r=5*t-4)))));r}

cp's OEIS Frontend

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

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A132854 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 4th power of an integer sequence such that 0 < c(n) <= 4*c(n-1) for n>0 with c(0)=1.

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

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