A261399 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

Offset

1,2

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Paul Drube, Raised k-Dyck paths, arXiv:2206.01194 [math.CO], 2022. See Appendix pp. 14-15.

Kyungpyo Hong, Ho Lee, Hwa Jeong Lee, and Seungsang 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)

a(n) = (6^n + 4)/10. - Paolo Xausa, Nov 17 2025

Mathematica

A261399[n_] := (6^n + 4)/10; Array[A261399, 25] (* or *)
LinearRecurrence[{7, -6}, {1, 4}, 25] (* Paolo Xausa, Nov 17 2025 *)

Crossrefs

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

Cf. A081341, A199412.

Sequence in context: A199033 A370695 A086682 * A396238 A155862 A088536

Adjacent sequences: A261396 A261397 A261398 * A261400 A261401 A261402

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 19 2015

Extensions

Name simplified by Paolo Xausa, Nov 17 2025

Status

approved