A144367 Shifts 3 places left under Dirichlet convolution.

1, 1, 1, 1, 2, 2, 3, 4, 6, 6, 10, 13, 16, 20, 32, 32, 46, 68, 73, 92, 152, 146, 200, 310, 312, 400, 658, 628, 832, 1328, 1302, 1664, 2740, 2604, 3400, 5500, 5300, 6812, 11178, 10600, 13770, 22388, 21412, 27540, 45132, 42824, 55392, 90352, 86048, 110784

Offset

1,5

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Formula

G.f.: x + x^2 + x^3 * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)). - Ilya Gutkovskiy, May 09 2019

Maple

k:= 3: with(numtheory): dck:= proc(b, c) proc(n, k) option remember; add(b(d, k) *c(n/d, k), d=`if`(n<0, {}, divisors(n))) end end: B:= dck(T, T): T:= (n, k)-> if n<=k then 1 else B(n-k, k) fi: a:= n-> T(n, k): seq(a(n), n=1..55);

Mathematica

dck[b_, c_][n_, k_] := dck[b, c][n, k] = Sum[b[d, k]*c[n/d, k], {d, If[n < 0, {}, Divisors[n]]}];
B = dck[T, T];
T[n_, k_] := If[n <= k, 1, B[n - k, k]];
a[n_] := T[n, 3];
Array[a, 55] (* Jean-François Alcover, Jun 11 2018, after Alois P. Heinz *)

Crossrefs

3rd column of A144374. Cf. A000005.

Sequence in context: A366843 A370805 A238860 * A370778 A075465 A011868

Adjacent sequences: A144364 A144365 A144366 * A144368 A144369 A144370

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 18 2008

Status

approved