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%I #85 Apr 15 2023 04:17:40
%S 1,6,11,16,21,26,31,36,41,46,51,56,61,66,71,76,81,86,91,96,101,106,
%T 111,116,121,126,131,136,141,146,151,156,161,166,171,176,181,186,191,
%U 196,201,206,211,216,221,226,231,236,241,246,251,256,261,266,271,276,281
%N a(n) = 5*n + 1.
%C Numbers ending in 1 or 6.
%C Apart from initial terms, same as 5n-14.
%C Complement of A047203; A027445(a(n)) mod 10 = 4. - _Reinhard Zumkeller_, Oct 23 2006
%C 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
%C Central terms of the triangle in A153125: a(n) = A153125(2*n+1, n+1). - _Reinhard Zumkeller_, Dec 20 2008
%C For n > 2, also the number of (not necessarily maximal) cliques in the n-Moebius ladder graph. - _Eric W. Weisstein_, Nov 29 2017
%C For n > 3, also the number of (not necessarily maximal) cliques in the n-prism graph. - _Eric W. Weisstein_, Nov 29 2017
%C For n >= 1, a(n) is the size of any hexagonal chain graph with n cells. - _Christian Barrientos_, _Sarah Minion_, Mar 07 2018
%C For n >= 1, a(n) is the number of possible outcomes of the summation when using n dice. - _Bram Kole_, Dec 24 2018
%C Numbers congruent to 1 (mod 5). - _Muniru A Asiru_, Jan 01 2019
%C 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
%H Ivan Panchenko, <a href="/A016861/b016861.txt">Table of n, a(n) for n = 0..1000</a>
%H J. Campbell, T. W. Mattman, R. Ottman, J. Pyzer, M. Rodrigues and S. Williams, <a href="https://arxiv.org/abs/math/0701422">Intrinsic knotting and linking of almost complete graphs</a>, arXiv:math/0701422 [math.GT], Jan 15 2007.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Clique.html">Clique</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrismGraph.html">Prism Graph</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: (1+4*x)/(1-x)^2.
%F Row sums of triangle A131843. - _Gary W. Adamson_, Jul 21 2007
%F a(n) = 2*a(n-1) - a(n-2) with a(0)=1, a(1)=6. - _Vincenzo Librandi_, Aug 01 2010
%F a(n) = A017293(n)/2 = A008587(n)+1. - _Wesley Ivan Hurt_, May 03 2014
%F E.g.f.: exp(x)*(1 + 5*x). - _Stefano Spezia_, Mar 23 2021
%F 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
%p A016861:=n->5*n+1; seq(A016861(n), n=0..100); # _Wesley Ivan Hurt_, May 03 2014
%t Range[1, 500, 5] (* _Vladimir Joseph Stephan Orlovsky_, May 26 2011 *)
%t LinearRecurrence[{2, -1}, {6, 11}, {0, 20}] (* _Eric W. Weisstein_, Nov 29 2017 *)
%t CoefficientList[Series[(1 + 4 x)/(-1 + x)^2, {x, 0, 20}], x] (* _Eric W. Weisstein_, Nov 29 2017 *)
%o (Haskell)
%o a016861 = (+ 1) . (* 5)
%o a016861_list = [1, 6 ..] -- _Reinhard Zumkeller_, Jun 16 2013
%o (PARI) a(n)=5*n+1 \\ _Charles R Greathouse IV_, Jul 10 2016
%o (GAP) a:=List([0..60],n->5*n+1);; Print(a); # _Muniru A Asiru_, Jan 01 2019
%Y Cf. A093562 ((5, 1) Pascal, column m=1).
%Y Cf. A000566 (partial sums).
%Y Cf. A000032, A000045, A001622, A131843, A342819.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 11 1996
%E More terms from _Reinhard Zumkeller_, Oct 23 2006
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