A379211 List of positive integers that are congruent to {2, 7, 8, 13} mod 15.

2, 7, 8, 13, 17, 22, 23, 28, 32, 37, 38, 43, 47, 52, 53, 58, 62, 67, 68, 73, 77, 82, 83, 88, 92, 97, 98, 103, 107, 112, 113, 118, 122, 127, 128, 133, 137, 142, 143, 148, 152, 157, 158, 163, 167, 172, 173, 178, 182, 187, 188, 193, 197, 202, 203, 208, 212, 217, 218, 223, 227, 232, 233, 238, 242, 247, 248, 253, 257, 262

Offset

1,1

Links

Table of n, a(n) for n=1..70.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n) = 15 + a(n-4); a(n) = - a(1-n).

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 6.

G.f.: x*(x^2 + 3*x + 1)*(2*x^2 - x + 2)/((1 + x)*(1 - x)^2*(1 + x^2)).

a(n)^2 = 15 * A379210(n) + 4.

For n >= 2, a(n-1) + a(n+1) = A072703(n).

It appears that a(n) + a(n+1) = (3/2) * A315211(n).

E.g.f.: (8 - 3*cos(x) + 5*(3*x - 1)*cosh(x) + 3*sin(x) + 5*(3*x - 2)*sinh(x))/4. - Stefano Spezia, Dec 23 2024

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*Pi/(5*sqrt(3)*phi), where phi is the golden ratio (A001622). - Amiram Eldar, Dec 24 2024

Maple

a := proc(n) option remember;
      `if`(n < 5, [0, 2, 7, 8, 13][n+1], 15 + a(n-4))
     end:
seq(a(n), n = 1..70);

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {2, 7, 8, 13, 17}, 70] (* Amiram Eldar, Dec 24 2024 *)

Crossrefs

Cf. A001622, A072703, A151972, A204542, A315211, A379210.

Sequence in context: A231625 A032927 A004717 * A308918 A226819 A270104

Adjacent sequences: A379208 A379209 A379210 * A379212 A379213 A379214

Keyword

nonn,easy

Author

Peter Bala, Dec 18 2024

Status

approved