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A357051
a(n) = Sum_{d|n} 3^(n-d).
2
1, 4, 10, 37, 82, 352, 730, 2998, 7291, 26488, 59050, 263170, 531442, 2127952, 5373460, 19669879, 43046722, 187086916, 387420490, 1607136634, 3878987860, 13947314752, 31381059610, 139902374692, 285916320883, 1129719740248, 2824682785300, 10460357985970
OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} 3^(k-1) * x^k/(1 - 3^(k-1) * x^k).
G.f.: Sum_{k>=1} x^k/(1 - (3 * x)^k).
MATHEMATICA
a[n_] := DivisorSum[n, 3^(n-#) &]; Array[a, 28] (* Amiram Eldar, Aug 23 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, 3^(n-d));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, 3^(k-1)*x^k/(1-3^(k-1)*x^k)))
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(3*x)^k)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Dec 20 2022
STATUS
approved