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A144817 Shifts left when Dirichlet convolution with a (DC:(b,a)->c) applied twice. 2
1, 1, 3, 9, 30, 90, 288, 864, 2647, 7968, 24084, 72252, 217467, 652401, 1958931, 5877333, 17637453, 52912359, 158754606, 476263818, 1428840972, 4286528100, 12859728804, 38579186412, 115738013592, 347214043476, 1041643435230, 3124930353363, 9374794990911 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..700

N. J. A. Sloane, Transforms

FORMULA

a(n) ~ c * 3^n, where c = 0.1365983596534181021630692308337960543393478528568767041107748567859... . - Vaclav Kotesovec, Sep 03 2014

MAPLE

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:= proc(n, k) local a, b, t; b[1]:= dc(a, a); for t from 2 to k do b[t]:= dc(b[t-1], a) od: a:= n-> `if`(n=1, 1, b[k](n-1)); a(n) end: a:= n-> A(n, 2): seq (a(n), n=1..30);

MATHEMATICA

dc[b_, c_] := Module[{f}, f[n_] := f[n] = Sum[b[d] c[n/d], {d, If[n<0, {}, Divisors[n]]}]; f];

A[n_, k_] := Module[{a, b, t}, b[1] = dc[a, a]; For[t = 2, t <= k, t++, b[t] = dc[b[t-1], a]]; a = Function[m, If[m==1, 1, b[k][m-1]]]; a[n]];

a[n_] := A[n, 2];

Array[a, 30] (* Jean-François Alcover, Dec 18 2020, after Maple *)

CROSSREFS

2nd column of A144823.

Sequence in context: A163129 A074003 A078844 * A337267 A337034 A250128

Adjacent sequences:  A144814 A144815 A144816 * A144818 A144819 A144820

KEYWORD

eigen,nonn

AUTHOR

Alois P. Heinz, Sep 21 2008

STATUS

approved

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Last modified March 1 02:43 EST 2021. Contains 341732 sequences. (Running on oeis4.)