A342610 a(0) = 0, a(1) = 1; a(2*n) = 5*a(n), a(2*n+1) = a(n) + a(n+1).

0, 1, 5, 6, 25, 11, 30, 31, 125, 36, 55, 41, 150, 61, 155, 156, 625, 161, 180, 91, 275, 96, 205, 191, 750, 211, 305, 216, 775, 311, 780, 781, 3125, 786, 805, 341, 900, 271, 455, 366, 1375, 371, 480, 301, 1025, 396, 955, 941, 3750, 961, 1055, 516, 1525, 521, 1080, 991

Offset

0,3

Links

Table of n, a(n) for n=0..55.

Formula

G.f.: x * Product_{k>=0} (1 + 5*x^(2^k) + x^(2^(k+1))).

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], 5 a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 55}]
nmax = 55; CoefficientList[Series[x Product[(1 + 5 x^(2^k) + x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

Crossrefs

Cf. A002487, A178569, A178590, A237711, A244643, A342611, A342614, A342615.

Sequence in context: A324485 A335827 A166591 * A160529 A039572 A033042

Adjacent sequences: A342607 A342608 A342609 * A342611 A342612 A342613

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2021

Status

approved