A261399 - OEIS

%I #17 Aug 03 2020 01:15:18

%S 1,4,22,130,778,4666,27994,167962,1007770,6046618,36279706,217678234,

%T 1306069402,7836416410,47018498458,282110990746,1692665944474,

%U 10155995666842,60935974001050,365615844006298,2193695064037786,13162170384226714,78973022305360282,473838133832161690

%N a(1)=1; thereafter a(n) = (2/5)*(9*6^(n-2)+1).

%C Partial sums of A081341. - _Klaus Purath_, Jul 28 2020

%H K. Hong, H. Lee, H. J. Lee and S. Oh, <a href="http://arxiv.org/abs/1312.4009">Small knot mosaics and partition matrices</a>, J. Phys.  A: Math. Theor. 47 (2014) 435201; arXiv:1312.4009 [math.GT], 2013-2014. See Cor. 2.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6).

%H <a href="/index/K#knots">Index entries for sequences related to knots</a>

%F G.f.: x-2*x^2*(-2+3*x) / ( (6*x-1)*(x-1) ). - _R. J. Mathar_, Aug 19 2015

%F a(n) = 2*A199412(n-2), n>1. - _R. J. Mathar_, Aug 19 2015

%F From _Klaus Purath_, Jul 28 2020: (Start)

%F a(n) = 7*a(n-1) - 6*a(n-2), n > 2.

%F a(n) = 6*a(n-1) - 2, n > 1.

%F a(n) = 3*6^(n-2) + a(n-1), n > 1.

%F (End)

%Y The number 22, the third term here, is the same 22 seen in A261400 and illustrated in a link in that entry.

%Y Cf. A199412.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Aug 19 2015