A132853 -id:A132853 - cp's OEIS frontend

A132852 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution square of an integer sequence such that 0 < c(n) <= 2*c(n-1) for n>0 with c(0)=1.

1, 1, 2, 4, 14, 62, 462, 5380, 105626, 3440686, 196429906, 19603795552, 3496015313038, 1120368106124268, 653253602487886098, 697073727912597623594, 1371575342274982257650434

Offset: 0

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

nonn

Equals the number of nodes at generation n in the 2-convoluted tree. The minimal path in the 2-convoluted tree is A083952 and the maximal path is A132831. The 2-convoluted tree is defined as follows: tree of all finite sequences {c(k), k=0..n} that form the initial terms of a self-convolution square of some integer sequence such that 0 < c(n) <= 2*c(n-1) for n>0 with a(0)=1.

			a(n) counts the nodes in generation n of the following tree.
Generations 0..5 of the 2-convoluted tree are as follows;
The path from the root is shown, with child nodes enclosed in [].
GEN.0: [1];
GEN.1: 1->[2];
GEN.2: 1-2->[1,3];
GEN.3:
1-2-1->[2]
1-2-3->[2,4,6];
GEN.4:
1-2-1-2->[2,4]
1-2-3-2->[1,3]
1-2-3-4->[1,3,5,7]
1-2-3-6->[1,3,5,7,9,11];
GEN.5:
1-2-1-2-2->[2,4]
1-2-1-2-4->[2,4,6,8]
1-2-3-2-1->[2]
1-2-3-2-3->[2,4,6]
1-2-3-4-1->[2]
1-2-3-4-3->[2,4,6]
1-2-3-4-5->[2,4,6,8,10]
1-2-3-4-7->[2,4,6,8,10,12,14]
1-2-3-6-1->[2]
1-2-3-6-3->[2,4,6]
1-2-3-6-5->[2,4,6,8,10]
1-2-3-6-7->[2,4,6,8,10,12,14]
1-2-3-6-9->[2,4,6,8,10,12,14,16,18]
1-2-3-6-11->[2,4,6,8,10,12,14,16,18,20,22].
Each path in the tree from the root node forms the initial terms of a self-convolution square of a sequence with integer terms.

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

Cf. A132853, A132854, A132855, A132856.

Cf. A083952, A132831.

Extended by Martin Fuller, Sep 24 2007.

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

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

A132856 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 6th power of an integer sequence such that 0 < c(n) <= 6*c(n-1) for n>0 with c(0)=1.

Original entry on oeis.org

1, 1, 6, 108, 7614, 2451762, 3773520918, 28927494486144, 1137959521626242430, 234471053096681379609150, 257075108927481255273258364890, 1518584605077301579030226106654776268, 48819910122176867311132781943952677374210562

Offset: 0

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

nonn

The minimal path in the 5-convoluted tree is A083956.

Equals the number of nodes at generation n in the 6-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 6th power of some integer sequence such that 0 < c(n) <= 6*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 6-convoluted tree are as follows;
The path from the root is shown, with child nodes enclosed in [].
GEN.0: [1];
GEN.1: 1->[6];
GEN.2: 1-6->[3,9,15,21,27,33];
GEN.3:
1-6-3->[2,8,14]
1-6-9->[2,8,14,20,26,32,38,44,50]
1-6-15->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86]
1-6-21->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122]
1-6-27->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122,128,134,140,146,152,158]
1-6-33->[2,8,14,20,26,32,38,44,50,56,62,68,74,80,86,92,98,104,110,116,122,128,134,140,146,152,158,164,170,176,182,188,194].
Each path in the tree from the root node forms the initial terms of a self-convolution 6th power of a sequence of integer terms.

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

Cf. A132852, A132853, A132854, A132855; A083956.

Extended by Martin Fuller, Sep 24 2007

cp's OEIS Frontend

A132852 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution square of an integer sequence such that 0 < c(n) <= 2*c(n-1) for n>0 with c(0)=1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A132856 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution 6th power of an integer sequence such that 0 < c(n) <= 6*c(n-1) for n>0 with c(0)=1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions