A392561 Euler transform of A016116 = 2^floor(n/2).

1, 1, 2, 4, 7, 13, 23, 41, 70, 124, 209, 361, 605, 1029, 1710, 2876, 4746, 7896, 12965, 21381, 34916, 57176, 92922, 151206, 244661, 395981, 638092, 1027882, 1650049, 2646855, 4234073, 6766343, 10788443, 17182105, 27312397, 43363807, 68735325, 108820159

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Mathematica

lista[nn_]:=Module[{v}, v=Table[2^Floor[n/2], {n, 0, nn-2}]; CoefficientList[Series[Product[1/(1-x^k)^(v[[k]]), {k, 1, Length[v]}], {x, 0, Length[v]}], x]]; lista[40] (* Vincenzo Librandi, Jan 21 2026 *)

Prog

(PARI) lista(nn)= my(ET(v)= Vec(prod(k=1, #v, 1/(1-x^k+x*O(x^#v))^v[k]))); ET([ 2^(n\2) |n<-[0..nn-2]]);
(Magma) lista := function(nn) R<x> := PowerSeriesRing(Integers(), nn); return Coefficients(&*[1/(1 - x^k)^(2^((k-1) div 2)) : k in [1..nn-1]]); end function; lista(50); // Vincenzo Librandi, Jan 21 2026

Crossrefs

Cf. A016116, A358369 (same transform, but from n=1).

Sequence in context: A114832 A239553 A319255 * A136299 A208354 A003116

Adjacent sequences: A392558 A392559 A392560 * A392562 A392563 A392564

Keyword

nonn

Author

Ruud H.G. van Tol, Jan 16 2026

Status

approved