A007435 -id:A007435 - cp's OEIS frontend

A357238 Inverse Moebius transform of tribonacci numbers (A000073).

0, 1, 1, 3, 4, 9, 13, 27, 45, 86, 149, 285, 504, 941, 1710, 3163, 5768, 10662, 19513, 35978, 66026, 121565, 223317, 411053, 755480, 1390042, 2555802, 4701713, 8646064, 15904390, 29249425, 53801243, 98950246, 182003370, 334745794, 615704412, 1132436852, 2082895617, 3831006934

Offset: 1

Ilya Gutkovskiy, Sep 19 2022

nonn

Cf. A000073, A007435, A357239.

nmax = 39; CoefficientList[Series[Sum[x^(2 k)/(1 - x^k - x^(2 k) - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

f(n) = ([0, 1, 0; 0, 0, 1; 1, 1, 1]^n)[1, 3]; \\ A000073
a(n) = sumdiv(n, d, f(d)); \\ Michel Marcus, Sep 20 2022

G.f.: Sum_{k>=1} x^(2*k) / (1 - x^k - x^(2*k) - x^(3*k)).
G.f.: Sum_{k>=1} A000073(k) * x^k / (1 - x^k).
a(n) = Sum_{d|n} A000073(d).

A357239 Inverse Moebius transform of tetranacci number (A000078).

Original entry on oeis.org

0, 0, 1, 1, 2, 5, 8, 16, 30, 58, 108, 214, 401, 781, 1493, 2888, 5536, 10705, 20569, 39707, 76433, 147420, 283953, 547566, 1055028, 2034029, 3919974, 7556717, 14564533, 28075593, 54114452, 104311848, 201062094, 387564973, 747044844, 1439986130, 2775641472, 5350241528, 10312882883

Offset: 1

Ilya Gutkovskiy, Sep 19 2022

nonn

Cf. A000078, A007435, A357238.

nmax = 39; CoefficientList[Series[Sum[x^(3 k)/(1 - x^k - x^(2 k) - x^(3 k) - x^(4 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest

G.f.: Sum_{k>=1} x^(3*k) / (1 - x^k - x^(2*k) - x^(3*k) - x^(4*k)).
G.f.: Sum_{k>=1} A000078(k) * x^k / (1 - x^k).
a(n) = Sum_{d|n} A000078(d).

A128589 A051731 * A127647.

Original entry on oeis.org

1, 1, 1, 1, 0, 2, 1, 1, 0, 3, 1, 0, 0, 0, 5, 1, 1, 2, 0, 0, 8, 1, 0, 0, 0, 0, 0, 13, 1, 1, 0, 3, 0, 0, 0, 21, 1, 0, 2, 0, 0, 0, 0, 0, 34, 1, 1, 0, 0, 5, 0, 0, 0, 0, 55

Offset: 1

Gary W. Adamson, Mar 11 2007

Row sums = A007435: (1, 2, 3, 5, 6, 12, 14, ...), inverse Moebius transform of the Fibonacci numbers.

			First few rows of the triangle:
  1;
  1, 1;
  1, 0, 2;
  1, 1, 0, 3;
  1, 0, 0, 0, 5;
  1, 1, 2, 0, 0, 8;
  ...

Cf. A051731, A127647, A007435.

Inverse Moebius transform of A127647, as infinite lower triangular matrices.

cp's OEIS Frontend

A357238 Inverse Moebius transform of tribonacci numbers (A000073).

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A357239 Inverse Moebius transform of tetranacci number (A000078).

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A128589 A051731 * A127647.

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