A144366 Shifts 2 places left under Dirichlet convolution.

1, 1, 1, 2, 2, 5, 4, 12, 8, 28, 17, 60, 34, 134, 68, 276, 140, 580, 280, 1186, 560, 2436, 1128, 4906, 2256, 9976, 4516, 20020, 9048, 40324, 18096, 80860, 36192, 162320, 72418, 324920, 144852, 651177, 289704, 1302914, 579476, 2608360, 1158952

Offset

1,4

Comments

Appears to be essentially the same as a sequence in Section 2.2 of Baril-Ramirez. - N. J. A. Sloane, Feb 18 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Jean-Luc Baril and José L. Ramírez, Knight's paths towards Catalan numbers, Univ. Bourgogne Franche-Comté (2022). Also arXiv:2206.12087, Jan 2023.

N. J. A. Sloane, Transforms

Formula

G.f.: x + x^2 * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)). - Ilya Gutkovskiy, May 09 2019

Maple

k:= 2: 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..50);

Mathematica

k = 2; dck[b_, c_][n_, k_] := dck[b, c][n, k] = DivisorSum[n, b[#, k] * c[n/#, k]&]; B = dck[T, T]; T[n_, k_] :=  If[n <= k, 1, B[n-k, k]]; a[n_] := T[n, k]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Apr 05 2017, translated from Maple *)

Crossrefs

2nd column of A144374. Cf. A000005.

Sequence in context: A124506 A264687 A112471 * A054156 A238834 A284686

Adjacent sequences: A144363 A144364 A144365 * A144367 A144368 A144369

Keyword

eigen,nonn

Author

Alois P. Heinz, Sep 18 2008

Status

approved