A121811 a(n) is the floor of the first component of M^n * (0, 1, 2, 3) where M is the matrix [[c, 1/2, 1/2, 1/2], [1/2, c, 1/2, 1/2], [1/2, 1/2, c, 1/2], [1/2, 1/2, 1/2, c]] and c=sqrt(3)/2.

0, 3, 8, 19, 46, 111, 263, 622, 1473, 3485, 8246, 19512, 46166, 109230, 258441, 611480, 1446777, 3423112, 8099170, 19162842, 45339771, 107275050, 253815495, 600533909, 1420878484, 3361834590, 7954186044, 18819806248, 44528139677, 105354709660, 249271919464, 589783693902

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Mathematica

M = N[Abs[MatrixPower[{{0, 1, 1, 1}, {1, 0, 1, 1}, {1, 1, 0, 1}, {1, 1, 1, 0}}, 1/2]]]
v[1] = {0, 1, 2, 3}
v[n_] := v[n] = M.v[n - 1]
Table[Floor[v[n][[1]]], {n, 1, 50}]

Prog

(PARI) B(n)={concat([0, 0, 0], Vec(1/((1 - 6*x + 6*x^2)*(1 + 2*x - 2*x^2)) + O(x^n)))}
seq(n)={my(v=B(n)); vector(n, k, (3*(v[k+2]-2*v[k+1]) + sqrtint(108*(v[k+1]-v[k])^2))\2^(k-2))} \\ Andrew Howroyd, Jan 12 2025

Crossrefs

Cf. A120471.

Sequence in context: A309537 A126874 A284942 * A370033 A244208 A296329

Adjacent sequences: A121808 A121809 A121810 * A121812 A121813 A121814

Keyword

nonn,easy,less

Author

Roger L. Bagula, Aug 30 2006

Extensions

Name clarified by Sean A. Irvine, Jan 12 2025

a(30) onwards from Andrew Howroyd, Jan 12 2025

Status

approved