A084508 Partial sums of A084509. Positions of ones in the first differences of A084506.

0, 1, 3, 9, 33, 129, 513, 2049, 8193, 32769, 131073, 524289, 2097153, 8388609, 33554433, 134217729, 536870913, 2147483649, 8589934593, 34359738369, 137438953473, 549755813889, 2199023255553, 8796093022209, 35184372088833

Offset: 0

Author

Antti Karttunen, Jun 02 2003

Keywords

• nonn

Links

• Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
• Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A084506, A084509, A087289.

Programs

Mathematica

LinearRecurrence[{5,-4},{0,1,3,9},30] (* Harvey P. Dale, May 21 2021 *)

Formula

a(n) = n for n < 2, a(n) = 2^(2*n - 3) + 1 = A087289(n-2) for n >= 2. - Antti Karttunen, Oct 24 2012 [Corrected by Petros Hadjicostas, Aug 02 2020]

From Chai Wah Wu, Jan 28 2021: (Start)

a(n) = 5*a(n-1) - 4*a(n-2) for n > 3.

G.f.: x*(-2*x^2 - 2*x + 1)/((x - 1)*(4*x - 1)). (End)