A083953 -id:A083953 - cp's OEIS frontend

A083946 Least integer coefficients of A(x), where 1<=a(n)<=6, such that A(x)^(1/6) consists entirely of integer coefficients.

1, 6, 3, 2, 3, 6, 6, 6, 3, 4, 6, 6, 6, 6, 3, 4, 6, 6, 3, 6, 6, 2, 3, 6, 6, 6, 3, 4, 6, 6, 2, 6, 6, 6, 6, 6, 6, 6, 3, 4, 6, 6, 4, 6, 6, 2, 6, 6, 4, 6, 3, 2, 3, 6, 6, 6, 3, 4, 3, 6, 3, 6, 3, 4, 6, 6, 2, 6, 3, 6, 3, 6, 1, 6, 6, 4, 6, 6, 2, 6, 6, 2, 6, 6, 3, 6, 3, 4, 6, 6, 1, 6, 6, 6, 6, 6, 6, 6, 3, 2, 6, 6, 6, 6, 3

Offset: 0

Paul D. Hanna, May 09 2003

nonn

More generally, "least integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m>0. Is this sequence periodic?

Robert G. Wilson v, Table of n, a(n) for n = 0..3000.
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Cf. A083952, A083953, A083954, A083945.

a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/6), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *)

More terms from Robert G. Wilson v, Jul 26 2005

A083947 Integer coefficients of A(x), where 1<=a(n)<=7, such that A(x)^(1/7) consists entirely of integer coefficients.

Original entry on oeis.org

1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 4, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 3, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7, 2, 7, 7, 7, 7, 7, 7, 5, 7, 7, 7, 7, 7, 7, 1, 7, 7, 7, 7, 7, 7

Offset: 0

Paul D. Hanna, May 09 2003

nonn

More generally the sequence, "integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m. Are these sequences periodic?

Robert G. Wilson v, Table of n, a(n) for n = 0..3000.

Cf. A083952, A083953, A083954, A083955, A083956, A083948, A083949, A083950.

a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/7), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *)

More terms from Robert G. Wilson v, Jul 26 2005

A084067 Integer coefficients of A(x), where 1<=a(n)<=12, such that A(x)^(1/12) consists entirely of integer coefficients.

Original entry on oeis.org

1, 12, 6, 4, 9, 12, 4, 12, 12, 8, 6, 12, 6, 12, 12, 12, 12, 12, 8, 12, 9, 12, 12, 12, 12, 12, 6, 12, 6, 12, 10, 12, 6, 12, 12, 12, 2, 12, 6, 8, 6, 12, 12, 12, 12, 4, 12, 12, 8, 12, 12, 8, 3, 12, 4, 12, 12, 4, 12, 12, 9, 12, 6, 4, 6, 12, 4, 12, 12, 12, 12, 12, 2, 12, 6, 12, 3, 12, 6, 12, 3, 8

Offset: 0

Paul D. Hanna, May 10 2003

nonn

More generally, the sequence: "integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m>0. Are these sequences ever periodic?

Robert G. Wilson v, Table of n, a(n) for n = 0..3000.

Cf. A083952, A083953, A083954, A083955, A083956, A083947 A083948, A083949, A083950, A084066.

a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/12), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 81}] (* Robert G. Wilson v *)

More terms from Robert G. Wilson v, Jul 26 2005

A083945 Least integer coefficients of A(x), where 1<=a(n)<=5, such that A(x)^(1/5) consists entirely of integer coefficients.

Original entry on oeis.org

1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 4, 5, 5, 5, 5, 3, 5, 5, 5, 5, 2, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 2, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 2, 5, 5, 5, 5, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 1, 5, 5, 5, 5, 3, 5, 5, 5, 5, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 5, 5, 5, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5

Offset: 0

Paul D. Hanna, May 09 2003

nonn

More generally, "least integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m>0. Is this sequence periodic?

Robert G. Wilson v, Table of n, a(n) for n = 0..3000.
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

Cf. A083952, A083953, A083954, A083946.

a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/5), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 104}] (* Robert G. Wilson v *)

More terms from Robert G. Wilson v, Jul 26 2005

A106216 Coefficients of g.f. A(x) where 0 <= a(n) <= 2 for all n>1, with initial terms {1,3}, such that A(x)^(1/3) consists entirely of integer coefficients.

Original entry on oeis.org

1, 3, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0

Offset: 0

Paul D. Hanna, May 01 2005

nonn

The self-convolution cube-root equals A106219. Positions of 1's is given by A106217. Positions of 2's is given by A106218. What is the frequency of occurrence of the 1's and 2's?

			A(x)^(1/3) = 1 + 1x - 1x^2 + 2x^3 - 4x^4 + 9x^5 - 21x^6 + 53x^6 -+...

Cf. A106217, A106218, A106219, A083953.

{a(n)=local(A=1+3*x);if(n==0,1,if(n==1,3, for(j=2,n, for(k=0,2,t=polcoeff((A+k*x^j+x*O(x^j))^(1/3),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,n)))}

A(z)=0 at z=-0.322846893915891638743032676733152456643928599...

A084066 Least integer coefficients of A(x), where 1<=a(n)<=11, such that A(x)^(1/11) consists entirely of integer coefficients.

Original entry on oeis.org

1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 1, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 4, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 5, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 5, 11, 11, 11, 11, 11

Offset: 0

Paul D. Hanna, May 10 2003

nonn

More generally, the sequence: "integer coefficients of A(x), where 1<=a(n)<=m, such that A(x)^(1/m) consists entirely of integer coefficients", appears to have a unique solution for all m>0. Are these sequences ever periodic?

Robert G. Wilson v, Table of n, a(n) for n = 0..3000.

Cf. A083952, A083953, A083954, A083955, A083956, A083947, A083948, A083949, A083950, A084067.

a[0] = 1; a[n_] := a[n] = Block[{k = 1, s = Sum[a[i]*x^i, {i, 0, n-1}]}, While[ Union[ IntegerQ /@ CoefficientList[ Series[(s+k*x^n)^(1/11), {x, 0, n}], x]] != {True}, k++ ]; k]; Table[ a[n], {n, 0, 71}] (* Robert G. Wilson v *)

a(k)=0 (mod 11) when k not= 0 (mod 11); a(0)=1, a(11)=1, a(22)=7, a(33)=4, a(44)=9, a(55)=5, a(66)=5, ...

More terms from Robert G. Wilson v, Jul 26 2005

A132853 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution cube of an integer sequence such that 0 < c(n) <= 3*c(n-1) for n>0 with c(0)=1.

Original entry on oeis.org

1, 1, 3, 18, 180, 4347, 245511, 33731424, 11850958449, 10823718435525, 26127739209077469, 169071160476526474689, 2962647736390311022542681, 141814999458311839862777779311, 18682218330844513414826192858258922

Offset: 0

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

nonn

Equals the number of nodes at generation n in the 3-convoluted tree. The minimal path in the 3-convoluted tree is A083953 and the maximal path is A132835. The 3-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 cube of some integer sequence such that 0 < c(n) <= 3*c(n-1) for n>0 with a(0)=1.

			a(n) counts the nodes in generation n of the following tree.
Generations 0..4 of the 3-convoluted tree are as follows;
The path from the root is shown, with child nodes enclosed in [].
GEN.0: [1];
GEN.1: 1->[3];
GEN.2: 1-3->[3,6,9];
GEN.3:
1-3-3->[1,4,7]
1-3-6->[1,4,7,10,13,16]
1-3-9->[1,4,7,10,13,16,19,22,25];
GEN.4:
1-3-3-1->[3]
1-3-3-4->[3,6,9,12]
1-3-3-7->[3,6,9,12,15,18,21]
1-3-6-1->[3]
1-3-6-4->[3,6,9,12]
1-3-6-7->[3,6,9,12,15,18,21]
1-3-6-10->[3,6,9,12,15,18,21,24,27,30]
1-3-6-13->[3,6,9,12,15,18,21,24,27,30,33,36,39]
1-3-6-16->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48]
1-3-9-1->[3]
1-3-9-4->[3,6,9,12]
1-3-9-7->[3,6,9,12,15,18,21]
1-3-9-10->[3,6,9,12,15,18,21,24,27,30]
1-3-9-13->[3,6,9,12,15,18,21,24,27,30,33,36,39]
1-3-9-16->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48]
1-3-9-19->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57]
1-3-9-22->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66 ]
1-3-9-25->[3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75].
Each path in the tree from the root node forms the initial terms of
a self-convolution cube of a sequence of integer terms.

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

Cf. A132852, A132854, A132855, A132856.

Cf. A083953, A132835.

Extended by Martin Fuller, Sep 24 2007.

A111603 Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the antidiagonal read from upper right to lower left.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 4, 1, 1, 2, 1, 2, 5, 1, 1, 2, 3, 4, 5, 6, 1, 1, 1, 3, 3, 5, 3, 7, 1, 1, 2, 3, 4, 5, 2, 7, 8, 1, 1, 2, 3, 4, 1, 3, 7, 4, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 1, 1, 3, 1, 5, 6, 7, 2, 3, 5, 11, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 1, 1, 3, 4, 5, 3, 1, 4, 9, 10

Offset: 1

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

			Table begins
k= 0 1 2 3 4 5 6 7 8 9 10 11 12 13
n\
1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2| 1 2 1 2 2 2 1 2 2 2 1 2 1 2
3| 1 3 3 1 3 3 3 3 3 3 3 3 1 3
4| 1 4 2 4 3 4 4 4 1 4 4 4 3 4
5| 1 5 5 5 5 1 5 5 5 5 4 5 5 5
6| 1 6 3 2 3 6 6 6 3 4 6 6 6 6
7| 1 7 7 7 7 7 7 1 7 7 7 7 7 7
8| 1 8 4 8 2 8 4 8 7 8 8 8 4 8
9| 1 9 9 3 9 9 3 9 9 1 9 9 6 9
10| 1 10 5 10 10 2 5 10 10 10 3 10 5 10
11| 1 11 11 11 11 11 11 11 11 11 11 1 11 11
12| 1 12 6 4 9 12 4 12 12 8 6 12 6 12
13| 1 13 13 13 13 13 13 13 13 13 13 13 13 1
14| 1 14 7 14 7 14 14 2 7 14 14 14 14 14
15| 1 15 15 5 15 3 10 15 15 10 15 15 5 15
16| 1 16 8 16 4 16 8 16 10 16 8 16 12 16

Cf. A111613, A083952, A083953, A083954, A083945, A083946, A083947, A083948, A083949, A083950, A084066, A084067.

Cf. A109626, A111604.

f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[ a[j], {j, 0, 32}]]; g[n_, m_] := f[n][[m]]; Flatten[ Table[ f[i, n - i], {n, 15}, {i, n - 1, 1, -1}]]

A111604 Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the antidiagonal read zig-zag.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 4, 3, 2, 1, 1, 2, 1, 2, 5, 1, 1, 6, 5, 4, 3, 2, 1, 1, 1, 3, 3, 5, 3, 7, 1, 1, 8, 7, 2, 5, 4, 3, 2, 1, 1, 2, 3, 4, 1, 3, 7, 4, 9, 1, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 3, 1, 5, 6, 7, 2, 3, 5, 11, 1, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 1, 1, 3, 4, 5, 3, 1, 4, 9, 10, 11

Offset: 1

Paul D. Hanna and Robert G. Wilson v, Aug 01 2005

T(n,n)=T(n,n+2)=A111627.

			Table begins
\k...0...1....2....3....4....5....6....7....8....9...10...11...12...13
n\
1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2| 1 2 1 2 2 2 1 2 2 2 1 2 1 2
3| 1 3 3 1 3 3 3 3 3 3 3 3 1 3
4| 1 4 2 4 3 4 4 4 1 4 4 4 3 4
5| 1 5 5 5 5 1 5 5 5 5 4 5 5 5
6| 1 6 3 2 3 6 6 6 3 4 6 6 6 6
7| 1 7 7 7 7 7 7 1 7 7 7 7 7 7
8| 1 8 4 8 2 8 4 8 7 8 8 8 4 8
9| 1 9 9 3 9 9 3 9 9 1 9 9 6 9
10| 1 10 5 10 10 2 5 10 10 10 3 10 5 10
11| 1 11 11 11 11 11 11 11 11 11 11 1 11 11
12| 1 12 6 4 9 12 4 12 12 8 6 12 6 12
13| 1 13 13 13 13 13 13 13 13 13 13 13 13 1
14| 1 14 7 14 7 14 14 2 7 14 14 14 14 14
15| 1 15 15 5 15 3 10 15 15 10 15 15 5 15
16| 1 16 8 16 4 16 8 16 10 16 8 16 12 16

Cf. A111613, A083952, A083953, A083954, A083945, A083946, A083947, A083948, A083949, A083950, A084066, A084067.

Cf. A109626, A111603.

f[n_] := f[n] = Block[{a}, a[0] = 1; a[l_] := a[l] = Block[{k = 1, s = Sum[ a[i]*x^i, {i, 0, l - 1}]}, While[ IntegerQ[ Last[ CoefficientList[ Series[(s + k*x^l)^(1/n), {x, 0, l}], x]]] != True, k++ ]; k]; Table[a[j], {j, 0, 32}]]; g[n_, m_] := f[n][[m]];

A196306 Coefficients of g.f. A(x) where -1 <= a(n) <= 1 for all n>1, with initial terms {1,3}, such that A(x)^(1/3) consists entirely of integer coefficients.

Original entry on oeis.org

1, 3, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0

Offset: 0

Paul D. Hanna, Oct 01 2011

sign

A(z) = 0 at z = -0.3218604126 5330206348 1666946119 2701743677 6909817084 3826086189 5315539535 3583969883 ...

			G.f.: A(x) = 1 + 3*x + x^3 - x^6 - x^9 - x^12 - x^18 + x^21 - x^24 - x^30 - x^33 + x^39 - x^42 - x^45 + x^48 + x^54 - x^60 - x^66 - x^69 + x^72 - x^75 + x^84 - x^87 - x^90 - x^93 - x^96 - x^102 + x^108 - x^114 - x^126 + x^132 - x^135 - x^138 + x^141 - x^144 - x^147 - x^153 - x^159 - x^162 + x^165 - x^168 - x^171 + x^174 - x^180 - x^183 + x^186 - x^189 - x^192 + x^195 +...
where
A(x)^(1/3) = 1 + x - x^2 + 2*x^3 - 4*x^4 + 9*x^5 - 22*x^6 + 55*x^7 - 142*x^8 + 375*x^9 - 1009*x^10 + 2753*x^11 - 7599*x^12 + 21178*x^13 - 59509*x^14 + 168401*x^15 - 479477*x^16 + 1372536*x^17 - 3947678*x^18 + 11402376*x^19 - 33059314*x^20 + 96177750*x^21 +...+ A196307(n)*x^n +...

Paul D. Hanna, Table of n, a(n) for n = 0..1001

Cf. A196307 (cube-root), A196308 (trisection); variants: A106216, A083953.

{a(n)=local(A=1+3*x); if(n==0, 1, if(n%3==0,for(j=1, n, for(k=-1, 1, t=polcoeff((A+k*x^j+x*O(x^j))^(1/3), j);
if(denominator(t)==1, A=A+k*x^j; break)))); polcoeff(A+x*O(x^n), n))}

cp's OEIS Frontend

A083946 Least integer coefficients of A(x), where 1<=a(n)<=6, such that A(x)^(1/6) consists entirely of integer coefficients.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A083947 Integer coefficients of A(x), where 1<=a(n)<=7, such that A(x)^(1/7) consists entirely of integer coefficients.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A084067 Integer coefficients of A(x), where 1<=a(n)<=12, such that A(x)^(1/12) consists entirely of integer coefficients.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A083945 Least integer coefficients of A(x), where 1<=a(n)<=5, such that A(x)^(1/5) consists entirely of integer coefficients.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Extensions

A106216 Coefficients of g.f. A(x) where 0 <= a(n) <= 2 for all n>1, with initial terms {1,3}, such that A(x)^(1/3) consists entirely of integer coefficients.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Formula

A084066 Least integer coefficients of A(x), where 1<=a(n)<=11, such that A(x)^(1/11) consists entirely of integer coefficients.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A132853 Number of sequences {c(i), i=0..n} that form the initial terms of a self-convolution cube of an integer sequence such that 0 < c(n) <= 3*c(n-1) for n>0 with c(0)=1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A111603 Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the antidiagonal read from upper right to lower left.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A111604 Consider the array T(n, m) where the n-th row is the sequence of integer coefficients of A(x), where 1<=a(n)<=n, such that A(x)^(1/n) consists entirely of integer coefficients and where m is the (m+1)-th coefficient. This is the antidiagonal read zig-zag.