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A144367 Shifts 3 places left under Dirichlet convolution. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jun 11 2018, after Alois P. Heinz *)

CROSSREFS

3rd column of A144374. Cf. A000005.

Sequence in context: A093594 A008806 A238860 * A075465 A011868 A145813

Adjacent sequences:  A144364 A144365 A144366 * A144368 A144369 A144370

KEYWORD

eigen,nonn

AUTHOR

Alois P. Heinz, Sep 18 2008

STATUS

approved

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Last modified April 13 12:29 EDT 2021. Contains 342936 sequences. (Running on oeis4.)