A133726 Möbius transform of the Pell numbers (A000129).

1, 1, 4, 10, 28, 64, 168, 396, 980, 2348, 5740, 13780, 33460, 80612, 194992, 470424, 1136688, 2743160, 6625108, 15992040, 38613792, 93216616, 225058680, 543325464, 1311738092, 3166782500, 7645369060, 18457475260, 44560482148, 107578322912, 259717522848

Offset

1,3

Links

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

Formula

a(n) = Sum_{d|n} A008683(n/d)*A000129(d) = Sum_{k=1..n} A054525(n,k) * A000129(k).

G.f.: Sum_{k>=1} mu(k) * x^k / (1 - 2*x^k - x^(2*k)). - Ilya Gutkovskiy, Feb 06 2020

Example

a(4) = 10 = (0, -1, 0, 1) dot (1, 2, 5, 12) = (0, -2, 0, 12).

Maple

with(numtheory):
a:= n-> add(mobius(n/d)*(<<0|1>, <1|2>>^d. <<0, 1>>)[1, 1], d=divisors(n)):
seq(a(n), n=1..40);  # Alois P. Heinz, Sep 26 2011

Crossrefs

Cf. A000129, A054525, A256281.

Sequence in context: A092504 A340568 A038579 * A026534 A034920 A274597

Adjacent sequences: A133723 A133724 A133725 * A133727 A133728 A133729

Keyword

nonn

Author

Gary W. Adamson, Sep 21 2007

Status

approved