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A359204
a(n) = Sum_{d|n} (n/d) * 4^(n-d).
2
1, 9, 49, 289, 1281, 7041, 28673, 147969, 602113, 2951169, 11534337, 57876481, 218103809, 1056997377, 4113563649, 19394592769, 73014444033, 354385657857, 1305670057985, 6210524807169, 23571585826817, 108851659538433, 404620279021569, 1942025331015681
OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} x^k/(1 - (4 * x)^k)^2.
MATHEMATICA
a[n_] := DivisorSum[n, 4^(n-#)*n/# &]; Array[a, 24] (* Amiram Eldar, Aug 27 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, n/d*4^(n-d));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(4*x)^k)^2))
CROSSREFS
Cf. also A359112.
Sequence in context: A123270 A114040 A231178 * A090390 A199411 A069665
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 20 2022
STATUS
approved