A342615 a(0) = 0, a(1) = 1; a(2*n) = 9*a(n), a(2*n+1) = a(n) + a(n+1).

0, 1, 9, 10, 81, 19, 90, 91, 729, 100, 171, 109, 810, 181, 819, 820, 6561, 829, 900, 271, 1539, 280, 981, 919, 7290, 991, 1629, 1000, 7371, 1639, 7380, 7381, 59049, 7390, 7461, 1729, 8100, 1171, 2439, 1810, 13851, 1819, 2520, 1261, 8829, 1900, 8271, 8209, 65610, 8281, 8919, 2620

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

G.f.: x * Product_{k>=0} (1 + 9*x^(2^k) + x^(2^(k+1))).

Maple

N:= 100: # for a(0) to a(N)
g:= x*mul(1+9*x^(2^k)+x^(2^(k+1)), k=0..ilog2(N)):
S:= series(g, x, N+1):
seq(coeff(S, x, i), i=0..N); # Robert Israel, May 04 2023

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], 9 a[n/2], a[(n - 1)/2] + a[(n + 1)/2]]; Table[a[n], {n, 0, 51}]
nmax = 51; CoefficientList[Series[x Product[(1 + 9 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, A342610, A342611, A342614.

Sequence in context: A135332 A098325 A101242 * A033046 A025635 A116555

Adjacent sequences: A342612 A342613 A342614 * A342616 A342617 A342618

Keyword

nonn,look

Author

Ilya Gutkovskiy, Mar 16 2021

Status

approved