VOOZH about

URL: https://oeis.org/A287592

⇱ A287592 - OEIS

login
A287592
Number of connected induced subgraphs on the n-crown graph.
0
0, 2, 6, 31, 167, 806, 3588, 15233, 62973, 256504, 1036274, 4167659, 16719843, 66985946, 268173264, 1073184709, 4293787577, 17177378732, 68714233758, 274866896783, 1099488558975, 4397998276462, 17592085380956, 70368534462281, 281474540502837, 1125899000872736
OFFSET
0,2
COMMENTS
Extended to a(0)-a(2) using the closed form.
LINKS
Eric Weisstein's World of Mathematics, Crown Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
Index entries for linear recurrences with constant coefficients, signature (11, -47, 101, -116, 68, -16).
FORMULA
a(n) = (-1+2^n)^2-(n*(-7+2^(1+n)+n))/2.
a(n) = 11*a(n-1)-47*a(n-2)+101*a(n-3)-116*a(n-4)+68*a(n-5)-16*a(n-6).
G.f.: (x*(2-16*x+59*x^2-94*x^3+52*x^4))/((1-2*x)^2*(-1+x)^3*(-1+4*x)).
MATHEMATICA
Table[(2^n - 1)^2 - 1/2 n (2^(n + 1) + n - 7), {n, 0, 20}]
LinearRecurrence[{11, -47, 101, -116, 68, -16}, {2, 6, 31, 167, 806,
3588}, {0, 20}]
CoefficientList[Series[(x (2 - 16 x + 59 x^2 - 94 x^3 + 52 x^4))/((1 - 2 x)^2 (-1 + x)^3 (-1 + 4 x)), {x, 0, 20}], x]
CROSSREFS
Sequence in context: A231816 A058028 A216834 * A054141 A007710 A385025
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, May 26 2017
STATUS
approved