The On-Line Encyclopedia of Integer Sequences (OEIS)

A302654 revision #4

A302654

Number of minimum total dominating sets in the n-path graph.

0, 1, 2, 1, 1, 4, 3, 1, 2, 9, 4, 1, 3, 16, 5, 1, 4, 25, 6, 1, 5, 36, 7, 1, 6, 49, 8, 1, 7, 64, 9, 1, 8, 81, 10, 1, 9, 100, 11, 1, 10, 121, 12, 1, 11, 144, 13, 1, 12, 169, 14, 1, 13, 196, 15, 1, 14, 225, 16, 1, 15, 256, 17, 1, 16, 289, 18, 1, 17, 324, 19, 1, 18, 361, 20, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..76.

Eric Weisstein's World of Mathematics, Path Graph

Eric Weisstein's World of Mathematics, Total Dominating Set

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1).

FORMULA

a(n) = ((-1)^n*(n - 2)^2 + (6 + n)^2 - 2*(n - 2)*(n + 6)*cos(n*Pi/2) - 48*sin(n*Pi/2))/6.

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12).

MATHEMATICA

Table[Piecewise[{{1, Mod[n, 4] == 0}, {((n + 2)/4)^2, Mod[n, 4] == 2}, {(n - 1)/4, Mod[n, 4] == 1}, {(n + 5)/4, Mod[n, 4] == 3}}], {n, 20}]

Table[((-1)^n (n - 2)^2 + (6 + n)^2 - 2 (n - 2) (n + 6) Cos[n Pi/2] - 48 Sin[n Pi/2])/64, {n, 20}]

LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {0, 1, 2, 1, 1, 4, 3, 1, 2, 9, 4, 1}, 20]

CROSSREFS

Sequence in context: A370005 A294082 A129705 * A264831 A264728 A306790

Adjacent sequences: A302651 A302652 A302653 * A302655 A302656 A302657

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Apr 11 2018

STATUS

approved