cp's OEIS Frontend

Same as Pisot sequences E(1, 8), L(1, 8), P(1, 8), T(1, 8). Essentially same as Pisot sequences E(8, 64), L(8, 64), P(8, 64), T(8, 64). See A008776 for definitions of Pisot sequences.

If X_1, X_2, ..., X_n is a partition of the set {1..2n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1..2n} -> {1,2,3} such that for fixed y_1,y_2,...,y_n in {1,2,3} we have f(X_i)<>{y_i}, (i=1..n). - Milan Janjic, May 24 2007

This is the auto-convolution (convolution square) of A059304. - R. J. Mathar, May 25 2009

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 8-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

a(n) is equal to the determinant of a 3 X 3 matrix with rows 2^(n+2), 2^(n+1), 2^n; 2^(n+3), 2^(n+4), 2(n+3); 2^n, 2^(n+1), 2^(n+2) when it is divided by 144. - J. M. Bergot, May 07 2014

a(n) gives the number of small squares in the n-th iteration of the Sierpinski carpet fractal. Equivalently, the number of vertices in the n-Sierpinski carpet graph. - Allan Bickle, Nov 27 2022

Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0(37).

Continued fraction expansion of tanh(1/3).

If a 2-set Y and a 3-set Z are disjoint subsets of an n-set X then a(n-4) is the number of 3-subsets of X intersecting both Y and Z. - Milan Janjic, Sep 08 2007

Leaves of the Odd Collatz-Tree: a(n) has no odd predecessors in all '3x+1' trajectories where it occurs: A139391(2*k+1) <> a(n) for all k; A082286(n)=A006370(a(n)). - Reinhard Zumkeller, Apr 17 2008

Let random variable X have a uniform distribution on the interval [0,c] where c is a positive constant. Then, for positive integer n, the coefficient of determination between X and X^n is (6n+3)/(n+2)^2, that is, A016945(n)/A000290(n+2). Note that the result is independent of c. For the derivation of this result, see the link in the Links section below. - Dennis P. Walsh, Aug 20 2013

Positions of 3 in A020639. - Zak Seidov, Apr 29 2015

a(n+2) gives the sum of 6 consecutive terms of A004442 starting with A004442(n). - Wesley Ivan Hurt, Apr 08 2016

Numbers k such that Fibonacci(k) mod 4 = 2. - Bruno Berselli, Oct 17 2017

Also numbers k such that t^k == -1 (mod 7), where t is a member of A047389. - Bruno Berselli, Dec 28 2017

Essentially first differences of A120741.

Binomial transform of A169604.

Second binomial transform of A005053 without initial term 1.

Inverse binomial transform of A103333 without initial term 1.

Second inverse binomial transform of A013708.

Except for first term 3, these are the integers that satisfy phi(n) = 4*n/7. - Michel Marcus, Jul 14 2015

Number of distinct quadratic residues (QR) over Z_7^n such that gcd(QR, 7^n) = 1 where n >= 1. - Param Mayurkumar Parekh, Feb 11 2023

Fixed points of the mapping defined by A067585. In binary these numbers show a regular pattern: 0, 11, 11011, 11011011, 11011011011, etc.

From Reinhard Zumkeller, Feb 22 2010: (Start)

a(n) = A173593(6*n-5) for n > 0:

terms of A173593 beginning and ending with digits '11' in binary representation;

for n > 0: a(n) = A033129(3*n-1); a(n) - a(n-1) = A103333(n). (End)

Table starts

.....1.........3.............9.................27.....................81

.....3........24...........192...............1536..................12288

.....9.......192..........4080..............86688................1841856

....27......1536.........86688............4890528..............275895264

....81.....12288.......1841856..........275895264............41325395328

...243.....98304......39133824........15564399648..........6189975781728

...729....786432.....831474432.......878052505824........927173138866560

..2187...6291456...17666296320.....49534593003552.....138877768818516672

..6561..50331648..375354928128...2794452367733472...20801977386689522208

.19683.402653184.7975147677696.157646678048909856.3115849763962378244064

a(n) = A081341(n+1).

Essentially first differences of A125682.

Binomial transform of A005053 without initial term 1.

Second binomial transform of A164346.

Inverse binomial transform of A169634.

Second inverse binomial transform of A103333 without initial term 1.

Contribution from Reinhard Zumkeller, May 02 2010: (Start)

a(n) = 3*A000400(n) = A000400(n+1)/2;

subsequence of A003586; a(n)=A003586(A014105(n)) for n<6. (End)

a(n+1)=8^n/3+2^(n+1)/3 with g.f. (1-6x)/(1-10x+16x^2) counts walks of length 2n+1 between adjacent nodes of degrees 1 and 4 on the graph of the (7,4) Hamming code.

Equals INVERT transform of (1, 0, 3, 0, 3, 0, 3, ...). - Gary W. Adamson, Apr 27 2009

No term is divisible by 3. - Vladimir Joseph Stephan Orlovsky, Mar 24 2011

For n > 3, a(n) is the number of quaternary sequences of length n-1 starting with q(0) = 0, in which all triples (q(i), q(i+1), q(i+2)) contain digits 0 and 3; cf. A294627. - Wojciech Florek, Jul 30 2018

For n > 0, a(n) is the number of ways to tile a strip of length n with squares, dominoes, and two colors of trominoes, with the restriction that the first tile cannot be a domino. - Greg Dresden and Bora Bursalı, Aug 31 2023

Interleaving of A010701 and -A010701; signed version of A010701.

Essentially first differences of A010674.

Inverse binomial transform of 3 followed by A000004.

Second inverse binomial transform of A010701.

Third inverse binomial transform of A007283.

Fourth inverse binomial transform of A000244 without initial term 1.

Fifth inverse binomial transform of A164346.

Sixth inverse binomial transform of A005053 without initial term 1.

Seventh inverse binomial transform of A169604.

Eighth inverse binomial transform of A169634.

Ninth inverse binomial transform of A103333 without initial term 1.

Tenth inverse binomial transform of A013708.

Eleventh inverse binomial transform of A093138 without initial term 1.