A016861 a(n) = 5*n + 1.

1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, 101, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 201, 206, 211, 216, 221, 226, 231, 236, 241, 246, 251, 256, 261, 266, 271, 276, 281

Offset: 0

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• easy

Comments

Numbers ending in 1 or 6.

Apart from initial terms, same as 5n-14.

Complement of A047203; A027445(a(n)) mod 10 = 4. - Reinhard Zumkeller, Oct 23 2006

Campbell reference shows: "A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted." - Jonathan Vos Post, Jan 18 2007

Central terms of the triangle in A153125: a(n) = A153125(2*n+1, n+1). - Reinhard Zumkeller, Dec 20 2008

For n > 2, also the number of (not necessarily maximal) cliques in the n-Moebius ladder graph. - Eric W. Weisstein, Nov 29 2017

For n > 3, also the number of (not necessarily maximal) cliques in the n-prism graph. - Eric W. Weisstein, Nov 29 2017

For n >= 1, a(n) is the size of any hexagonal chain graph with n cells. - Christian Barrientos, Sarah Minion, Mar 07 2018

For n >= 1, a(n) is the number of possible outcomes of the summation when using n dice. - Bram Kole, Dec 24 2018

Numbers congruent to 1 (mod 5). - Muniru A Asiru, Jan 01 2019

Numbers k such that the k-th Fibonacci number, A000045(k), and the k-th Lucas number, A000032(k), end with the same decimal digit. - Amiram Eldar, Apr 15 2023

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• J. Campbell, T. W. Mattman, R. Ottman, J. Pyzer, M. Rodrigues and S. Williams, Intrinsic knotting and linking of almost complete graphs, arXiv:math/0701422 [math.GT], Jan 15 2007.
• Tanya Khovanova, Recursive Sequences.
• Eric Weisstein's World of Mathematics, Clique.
• Eric Weisstein's World of Mathematics, Moebius Ladder.
• Eric Weisstein's World of Mathematics, Prism Graph.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A093562 ((5, 1) Pascal, column m=1).

Cf. A000566 (partial sums).

Cf. A000032, A000045, A001622, A131843, A342819.

Programs

GAP

a:=List([0..60],n->5*n+1);; Print(a); # Muniru A Asiru, Jan 01 2019

Haskell

a016861 = (+ 1) . (* 5)
a016861_list = [1, 6 ..]  -- Reinhard Zumkeller, Jun 16 2013

Maple

A016861:=n->5*n+1; seq(A016861(n), n=0..100); # Wesley Ivan Hurt, May 03 2014

Mathematica

Range[1, 500, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
LinearRecurrence[{2, -1}, {6, 11}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[(1 + 4 x)/(-1 + x)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)

PARI

a(n)=5*n+1 \\ Charles R Greathouse IV, Jul 10 2016

Formula

G.f.: (1+4*x)/(1-x)^2.

Row sums of triangle A131843. - Gary W. Adamson, Jul 21 2007

a(n) = 2*a(n-1) - a(n-2) with a(0)=1, a(1)=6. - Vincenzo Librandi, Aug 01 2010

a(n) = A017293(n)/2 = A008587(n)+1. - Wesley Ivan Hurt, May 03 2014

E.g.f.: exp(x)*(1 + 5*x). - Stefano Spezia, Mar 23 2021

Sum_{n>=0} (-1)^n/a(n) = sqrt(2+2/sqrt(5))*Pi/10 + log(phi)/sqrt(5) + log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

Extensions

More terms from Reinhard Zumkeller, Oct 23 2006