A144368 Shifts 4 places left under Dirichlet convolution.

1, 1, 1, 1, 1, 2, 2, 3, 2, 6, 4, 8, 5, 14, 8, 22, 10, 32, 18, 51, 20, 72, 36, 116, 44, 152, 72, 258, 89, 314, 148, 548, 178, 660, 296, 1146, 364, 1340, 596, 2380, 728, 2716, 1202, 4880, 1456, 5508, 2404, 9912, 2932, 11088, 4808, 20128, 5868, 22276, 9636

Offset

1,6

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 + x^4 * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)). - Ilya Gutkovskiy, May 09 2019

Maple

k:= 4: 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, 4];
Array[a, 55] (* Jean-François Alcover, Jun 11 2018, after Alois P. Heinz *)

Crossrefs

4th column of A144374. Cf. A000005.

Sequence in context: A341105 A290309 A095757 * A094438 A156098 A294933

Adjacent sequences: A144365 A144366 A144367 * A144369 A144370 A144371

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 18 2008

Status

approved