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

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))

Crossrefs

Cf. A000203, A080267, A115607, A359203.

Cf. also A359112.

Sequence in context: A123270 A114040 A231178 * A090390 A199411 A069665

Adjacent sequences: A359201 A359202 A359203 * A359205 A359206 A359207

Keyword

nonn,easy

Author

Seiichi Manyama, Dec 20 2022

Status

approved