A381193 a(n) = (3*n-1)*(n^4-18*n^3+179*n^2-582*n+720)/120.

5, 6, 12, 33, 77, 153, 274, 460, 741, 1160, 1776, 2667, 3933, 5699, 8118, 11374, 15685, 21306, 28532, 37701, 49197, 63453, 80954, 102240, 127909, 158620, 195096, 238127, 288573, 347367, 415518, 494114, 584325, 687406, 804700, 937641, 1087757, 1256673, 1446114

Offset

1,1

Comments

For n > 2, a(n) is the number of connected minimal dominating sets in the n-Andrasfai graph.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Andrasfai Graph.

Eric Weisstein's World of Mathematics, Connected Graph.

Eric Weisstein's World of Mathematics, Minimum Dominating Set.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6).

G.f.: x*(5-24*x+51*x^2-49*x^3+14*x^4+6*x^5)/(-1+x)^6.

E.g.f.: 6 + exp(x)*(x^5/40 - 5*x^4/24 + 5*x^3/2 - 5*x^2 + 11*x - 6). - Stefano Spezia, Feb 17 2025

Mathematica

Table[(3 n - 1) (n^4 - 18 n^3 + 179 n^2 - 582 n + 720)/120, {n, 20}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {5, 6, 12, 33, 77, 153}, 20]
CoefficientList[Series[(5 - 24 x + 51 x^2 - 49 x^3 + 14 x^4 + 6 x^5)/(-1 + x)^6, {x, 0, 20}], x]

Prog

(Python)
def A381193(n): return n*(n*(n*(n*(3*n - 55) + 555) - 1925) + 2742)//120-6 # Chai Wah Wu, Feb 16 2025
(Magma) [(3*n-1)*(n^4-18*n^3+179*n^2-582*n+720)/120: n in [1..50]]; // Vincenzo Librandi, Mar 03 2025

Crossrefs

Sequence in context: A173074 A099473 A051572 * A344221 A348155 A047436

Adjacent sequences: A381190 A381191 A381192 * A381194 A381195 A381196

Keyword

nonn,easy

Author

Eric W. Weisstein, Feb 16 2025

Status

approved