A261399 - OEIS

A261399

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

1, 4, 22, 130, 778, 4666, 27994, 167962, 1007770, 6046618, 36279706, 217678234, 1306069402, 7836416410, 47018498458, 282110990746, 1692665944474, 10155995666842, 60935974001050, 365615844006298, 2193695064037786, 13162170384226714, 78973022305360282, 473838133832161690

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OFFSET

1,2

COMMENTS

Partial sums of A081341. - Klaus Purath, Jul 28 2020

LINKS

Table of n, a(n) for n=1..24.

K. Hong, H. Lee, H. J. Lee and S. Oh, Small knot mosaics and partition matrices, J. Phys. A: Math. Theor. 47 (2014) 435201; arXiv:1312.4009 [math.GT], 2013-2014. See Cor. 2.

Index entries for linear recurrences with constant coefficients, signature (7,-6).

Index entries for sequences related to knots

FORMULA

G.f.: x-2*x^2*(-2+3*x) / ( (6*x-1)*(x-1) ). - R. J. Mathar, Aug 19 2015

a(n) = 2*A199412(n-2), n>1. - R. J. Mathar, Aug 19 2015

From Klaus Purath, Jul 28 2020: (Start)

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

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

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

(End)

CROSSREFS

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