cp's OEIS Frontend

Define a sequence c(n) by c(0)=0, c(1)=1; thereafter c(n) = (c(n-2)*c(n-1)-1)/(c(n-2)+c(n-1)+2). Then it appears that (apart from signs), a(n) is the denominator of c(n). - Jonas Holmvall, Jun 21 2023

Hankel transform of A105864.

The sequence 1,1,2,8,... with general term 2^floor(n^2/3) is the Hankel transform of A109033. - Paul Barry, Dec 14 2008

See A105397 for definition of Fractal Jump Sequence.

From Vincenzo Librandi, Nov 13 2010: (Start)

First digit after the decimal point in the decimal expansion of (n^2 - 2)/3 (with n > 2). Examples:

for n=3, (3^2-2)/3 = 2.(3);

for n=4, (4^2-2)/3 = 4.(6);

for n=5, (5^2-2)/3 = 7.(6);

for n=6, (6^2-2)/3 = 11.(3);

for n=7, (7^2-2)/3 = 15.(6). (End)

Denominator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/3; numerator = A167816(n).

Continued fraction expansion of (33 + sqrt(2805))/66. - Klaus Brockhaus, May 06 2010

Self-inverse permutation of the natural numbers.

a(n) is a pairing function: a function that reversibly maps Z^{+} x Z^{+} onto Z^{+}, where Z^{+} is the set of integer positive numbers.

In general, let b(z) be a sequence of integers and denote number of antidiagonal table T(n,k) by z=n+k-1. Natural numbers placed in table T(n,k) by antidiagonals. The order of placement - by antidiagonal downwards, if b(z) is odd; by antidiagonal upwards, if b(z) is even. T(n,k) read by antidiagonals downwards. For A218890 -- the order of placement -- at the beginning m antidiagonals downwards, next m antidiagonals upwards and so on - b(z)=floor((z+m-1)/m). For this sequence b(z)=z^2 mod 3. (This comment should be edited for clarity, Joerg Arndt, Dec 11 2014)

a(n) is a component of the n-th partial product of 2 X 2 matrices with rows (0,1), (1, 1 + A130196(j)), j>=1.

The linear recurrence shows that these are three interleaved sequences (0,7,182,...), (1,23,599,...) and (2,53,1380,...) obeying simple recurrences of the form b(n) = 26*b(n-1) + b(n-2).

Row sums = A004277, (1, 2, 4, 6, 8, 10, ...). Binomial transform of (1, 1, 2, 2, 2, ...) = A000325, starting (1, 2, 5, 12, 27, 58, ...). Binomial transform of A130196 = A130197, a triangle with row sums = the Cullen numbers, A002064.

Permutation of the natural numbers. a(n) is a pairing function: a function that reversibly maps Z^{+} x Z^{+} onto Z^{+}, where Z^{+} is the set of integer positive numbers.In general, let b(z) be a sequence of integer numbers. Layer is pair of sides of square from T(1,n) to T(n,n) and from T(n,n) to T(n,1). Natural numbers placed in table T(n,k) layer by layer. The order of placement - layer is counterclockwise, if b(z) is odd; layer is clockwise if b(z) is even. T(n,k) read by antidiagonals.For A219159 - the order of the placement - at the beginning m layers counterclockwise, next m layers clockwise and so on - b(z)=floor((z-1)/m)+1. For this sequence b(z)=z^2 mod 3.