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A133726 Möbius transform of the Pell numbers (A000129). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
Sequence in context: A092504 A340568 A038579 * A026534 A034920 A274597
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Sep 21 2007
STATUS
approved

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Last modified March 3 03:04 EST 2024. Contains 370499 sequences. (Running on oeis4.)