A389178 a(n) = 3*2^n + 3*n + 1.

4, 10, 19, 34, 61, 112, 211, 406, 793, 1564, 3103, 6178, 12325, 24616, 49195, 98350, 196657, 393268, 786487, 1572922, 3145789, 6291520, 12582979, 25165894, 50331721, 100663372, 201326671, 402653266, 805306453, 1610612824, 3221225563, 6442451038, 12884901985

Offset

0,1

Comments

For n >= 3, also the number of mutual-visibility sets in the n-dipyramidal graph.

Links

Table of n, a(n) for n=0..32.

Eric Weisstein's World of Mathematics, Dipyramidal Graph.

Eric Weisstein's World of Mathematics, Visibility Polynomial.

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

G.f.: (-4+6*x+x^2)/((-1+x)^2*(-1+2*x)).

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

From Enrique Navarrete, Jan 25 2026: (Start)

a(n+1) - a(n) = 3*A000051(n).

E.g.f.: exp(x)*(3*exp(x) + 3*x + 1). (End)

Mathematica

Table[3 2^n + 3 n + 1, {n, 0, 20}]
LinearRecurrence[{4, -5, 2}, {10, 19, 34}, {0, 20}]
CoefficientList[Series[(-4 + 6 x + x^2)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x]

Crossrefs

Cf. A000051.

Sequence in context: A155368 A301155 A301215 * A155389 A155316 A346760

Adjacent sequences: A389175 A389176 A389177 * A389179 A389180 A389181

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 25 2025

Status

approved