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A144368 Shifts 4 places left under Dirichlet convolution. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified April 13 21:06 EDT 2021. Contains 342941 sequences. (Running on oeis4.)