A144316 Shifts left when Dirichlet convolution (DC:(b,b)->a) applied twice.

1, 1, 4, 16, 70, 280, 1168, 4672, 18884, 75632, 303368, 1213472, 4858064, 19432256, 77743040, 310975520, 1243959873, 4975839492, 19903598208, 79614392832, 318458493192, 1273834028832, 5095339755744, 20381359022976, 81525450936496, 326101803775384

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500

N. J. A. Sloane, Transforms

Formula

a(n) ~ c * 4^n, where c = 0.0724091505138381672774074945426621544789572745186499358668403190389... . - Vaclav Kotesovec, Sep 03 2014

Maple

k:=2: with(numtheory): dc:= proc(b, c) proc(n) option remember; add(b(d) *c(n/d), d=`if`(n<0, {}, divisors(n))) end end: a:='a': b[1]:= dc(a, a): for t from 2 to k do b[t]:= dc(b[t-1], b[t-1]) od: a:= n-> `if`(n=1, 1, b[k](n-1)): seq(a(n), n=1..30);

Mathematica

dc[b_, c_] := Module[{proc}, proc[n_] := proc[n] = Sum[b[d]*c[n/d], {d, If[n < 0, {}, Divisors[n]]}]; proc];
A[n_, k_] := Module[{a, b, t}, b[1] = dc[a, a]; For[t = 2, t <= k, t++, b[t] = dc[b[t-1], b[t-1]]]; a = Function[m, If[m == 1, 1, b[k][m-1]]]; a[n]];
a[n_] := A[n, 2];
Array[a, 30] (* Jean-François Alcover, Jun 11 2018, after Alois P. Heinz *)

Crossrefs

2nd column of A144324, 3rd column of A144823.

Sequence in context: A351186 A298048 A344267 * A180145 A133789 A151244

Adjacent sequences: A144313 A144314 A144315 * A144317 A144318 A144319

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 17 2008

Status

approved