A062051 -id:A062051 - cp's OEIS frontend

A338848 Number of compositions (ordered partitions) of n into distinct powers of 3.

1, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 6, 0, 0, 0, 0, 2, 6, 0, 6, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 6, 0, 0, 0, 0, 2, 6

Offset: 0

Ilya Gutkovskiy, Nov 11 2020

nonn

Index entries for sequences related to compositions

Cf. A000244, A039966, A062051, A062756, A078932, A093659.

a(n) = my(c=0,r); while(n, [n,r]=divrem(n,3); if(r==2,return(0)); c+=r); c!; \\ Kevin Ryde, Nov 14 2020

a(n) = A039966(n) * A062756(n)!. - Kevin Ryde, Nov 14 2020

A374626 Expansion of Product_{k>=0} 1 / (1 - 3*x^(3^k)).

Original entry on oeis.org

1, 3, 9, 30, 90, 270, 819, 2457, 7371, 22143, 66429, 199287, 597951, 1793853, 5381559, 16144947, 48434841, 145304523, 435914388, 1307743164, 3923229492, 11769690933, 35309072799, 105927218397, 317781662562, 953344987686, 2860034963058, 8580104911317

Offset: 0

Seiichi Manyama, Jul 14 2024

nonn

For generating functions Product_{k>=0} 1 / (1 - a*x^(b^k)) for the following values of (a,b) see: (1,2) A018819, (1,3) A062051, (2,2) A309728.

Cf. A117940.

my(N=30, x='x+O('x^N)); Vec(1/prod(k=0, logint(N,3), 1-3*x^3^k))

G.f. A(x) satisfies A(x) = A(x^3)/(1 - 3*x).

a(n) is divisible by 3 for n > 0.

A374627 Expansion of Product_{k>=0} 1 / (1 - x^(3^k))^3.

Original entry on oeis.org

1, 3, 6, 13, 24, 39, 64, 99, 144, 212, 303, 417, 578, 786, 1041, 1382, 1809, 2322, 2985, 3798, 4761, 5973, 7434, 9144, 11247, 13743, 16632, 20126, 24225, 28929, 34541, 41061, 48489, 57242, 67320, 78723, 92029, 107238, 124350, 144151, 166641, 191820, 220729, 253368, 289737, 331218, 377811

Offset: 0

Seiichi Manyama, Jul 14 2024

nonn

Cf. A062051, A171238, A309677.

my(N=50, x='x+O('x^N)); Vec(1/prod(k=0, logint(N, 3), 1-x^3^k)^3)

G.f. A(x) satisfies A(x) = A(x^3)/(1 - x)^3.

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A338848 Number of compositions (ordered partitions) of n into distinct powers of 3.

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A374626 Expansion of Product_{k>=0} 1 / (1 - 3*x^(3^k)).

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Author

Keywords

Crossrefs

Programs

PARI

Formula

A374627 Expansion of Product_{k>=0} 1 / (1 - x^(3^k))^3.

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Author

Keywords

Crossrefs

Programs

PARI

Formula