A298648 Number of smallest coverings of the n-dipyramidal graph by maximal cliques.

1, 4, 30, 12, 98, 28, 270, 60, 682, 124, 1638, 252, 3810, 508, 8670, 1020, 19418, 2044, 42966, 4092, 94162, 8188, 204750, 16380, 442314, 32764, 950214, 65532, 2031554, 131068, 4325310, 262140, 9174970, 524284, 19398582, 1048572, 40894386, 2097148, 85983150

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

Cf. A110654 (clique covering number of the n-dipyramidal graph).

Sequence in context: A213795 A159862 A364853 * A164820 A022387 A108559

Adjacent sequences: A298645 A298646 A298647 * A298649 A298650 A298651

Keyword

nonn,easy

Author

Eric W. Weisstein, Jun 18 2018

Extensions

Terms a(19) and beyond from Andrew Howroyd, Jun 27 2018

Status

approved