The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A303834 Number of total dominating sets in the n-gear graph. 0
 3, 21, 48, 161, 473, 1476, 4553, 14241, 44688, 141081, 447153, 1422596, 4539473, 14522361, 46556048, 149508801, 480810153, 1548053316, 4988972313, 16090635281, 51928966928, 167675418921, 541639730273, 1750245266436, 5657268819873, 18289912673001 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Extended to a(1)-a(2) using the formula/recurrence. LINKS Eric Weisstein's World of Mathematics, Gear Graph Eric Weisstein's World of Mathematics, Total Dominating Set Index entries for linear recurrences with constant coefficients, signature (4,2,-13,-6,4). FORMULA a(n) = 2*(-1)^n + 2^n*A000032(n) + A005248(n). a(n) = 4*a(n-1) + 2*a(n-2) - 13*a(n-3) - 6*a(n-4) + 4*a(n-5). G.f.: -x*(3+9*x-42*x^2-34*x^3+24*x^4) / ( (1+x)*(x^2-3*x+1)*(4*x^2+2*x-1) ). MATHEMATICA Table[2 (-1)^n + 2^n LucasL[n] + LucasL[2 n], {n, 20}] LinearRecurrence[{4, 2, -13, -6, 4}, {3, 21, 48, 161, 473}, 20] CoefficientList[Series[(-3 - 9 x + 42 x^2 + 34 x^3 - 24 x^4)/(-1 + 4 x + 2 x^2 - 13 x^3 - 6 x^4 + 4 x^5), {x, 0, 20}], x] CROSSREFS Sequence in context: A318211 A219069 A027499 * A340687 A152773 A039595 Adjacent sequences:  A303831 A303832 A303833 * A303835 A303836 A303837 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, May 02 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 15 02:21 EDT 2021. Contains 343909 sequences. (Running on oeis4.)