OFFSET
3,2
LINKS
Muniru A Asiru, Table of n, a(n) for n = 3..700
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Maximal Clique
Eric Weisstein's World of Mathematics, Minimum Clique Covering
Index entries for linear recurrences with constant coefficients, signature (0,6,0,-13,0,12,0,-4)
FORMULA
a(2*k) = 2^(k+1) - 4, a(2*k-1) = (2*k-1)*(2^k - 2) for k > 2. - Andrew Howroyd, Jun 27 2018
From Colin Barker, Jul 20 2019: (Start)
G.f.: x^3*(1 + 4*x + 24*x^2 - 12*x^3 - 69*x^4 + 8*x^5 + 60*x^6 - 20*x^8) / ((1 - x)^2*(1 + x)^2*(1 - 2*x^2)^2).
a(n) = (1 + (-1)^n)*(-2+2^(n/2)) + ((-1+(-1)^n)*(sqrt(2) - 2^(n/2))*n)/sqrt(2) for n>3.
a(n) = 6*a(n-2) - 13*a(n-4) + 12*a(n-6) - 4*a(n-8) for n>8.
(End)
MAPLE
seq(coeff(series((1+4*x+24*x^2-12*x^3-69*x^4+8*x^5+60*x^6-20*x^8)/(1-3*x^2+2*x^4)^2, x, n+1), x, n), n=0..38); # Muniru A Asiru, Jul 02 2018
MATHEMATICA
Join[{1}, Table[If[Mod[n, 2] == 0, 2, n] (2^Ceiling[n/2] - 2), {n, 4, 20}]]
Join[{1}, Table[2 (1 + (-1)^n) (2^(n/2 - 1) - 1) + (1 - (-1)^n) (2^((n - 1)/2) - 1) n, {n, 4, 20}]]
Join[{1}, LinearRecurrence[{0, 6, 0, -13, 0, 12, 0, -4}, {4, 30, 12, 98, 28, 270, 60, 682}, 20]]
CoefficientList[Series[(1 + 4 x + 24 x^2 - 12 x^3 - 69 x^4 + 8 x^5 + 60 x^6 - 20 x^8)/(1 - 3 x^2 + 2 x^4)^2, {x, 0, 20}], x]
PROG
(PARI) a(n)={if(n==3, 1, if(n%2, n, 2)*(2^ceil(n/2)-2))} \\ Andrew Howroyd, Jun 27 2018
(PARI) Vec(x^3*(1 + 4*x + 24*x^2 - 12*x^3 - 69*x^4 + 8*x^5 + 60*x^6 - 20*x^8) / ((1 - x)^2*(1 + x)^2*(1 - 2*x^2)^2) + O(x^45)) \\ Colin Barker, Jul 20 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 18 2018
EXTENSIONS
Terms a(19) and beyond from Andrew Howroyd, Jun 27 2018
STATUS
approved