OFFSET
0,2
COMMENTS
Old definition was: "a(n) = T(n,n), array T given by A048483".
Also the number of connected induced subgraphs in the n-sunlet graph. - Eric W. Weisstein, May 25 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Mohammed Aljohani, Sami Lazaar, Abdelwaheb Mhemdi, Neama Zidani, and Ahmed Aboubakr, Numerical Studies of Some Partial Orderings on a Set With Height at Most One, Bol. Soc. Paran. Mat. (2025) Vol. 43, 1-12. See p. 9.
Eric Weisstein's World of Mathematics, Sunlet Graph.
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph.
Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).
FORMULA
a(n) = (n+1)*2^n - n. - Vladeta Jovovic, Feb 28 2003
From Colin Barker, Nov 26 2014: (Start)
a(n) = 6*a(n-1) - 13*a(n-2) + 12*a(n-3) - 4*a(n-4).
G.f.: -(4*x^3-5*x^2+3*x-1)/((x-1)^2*(2*x-1)^2). (End)
E.g.f.: exp(x)*(exp(x)*(1+2*x) - x). - Elmo R. Oliveira, Oct 27 2025
MATHEMATICA
Table[(n + 1) 2^n - n, {n, 20}] (* Eric W. Weisstein, May 25 2017 *)
Table[2^n + (2^n - 1) n, {n, 20}] (* Eric W. Weisstein, May 25 2017 *)
LinearRecurrence[{6, -13, 12, -4}, {3, 10, 29, 76}, 20] (* Eric W. Weisstein, May 25 2017 *)
PROG
(Magma) [(n+1)*2^n-n: n in [0..30]]; // Vincenzo Librandi, Sep 26 2011
(PARI) Vec(-(4*x^3-5*x^2+3*x-1)/((x-1)^2*(2*x-1)^2) + O(x^100)) \\ Colin Barker, Nov 26 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Description changed to more explicit formula by Eric W. Weisstein, May 25 2017
STATUS
approved