A359204 - OEIS

A359204

a(n) = Sum_{d|n} (n/d) * 4^(n-d).

1, 9, 49, 289, 1281, 7041, 28673, 147969, 602113, 2951169, 11534337, 57876481, 218103809, 1056997377, 4113563649, 19394592769, 73014444033, 354385657857, 1305670057985, 6210524807169, 23571585826817, 108851659538433, 404620279021569, 1942025331015681

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..24.

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))