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%I #90 Dec 31 2022 05:38:30
%S 1,11,21,31,41,51,61,71,81,91,101,111,121,131,141,151,161,171,181,191,
%T 201,211,221,231,241,251,261,271,281,291,301,311,321,331,341,351,361,
%U 371,381,391,401,411,421,431,441,451,461,471,481,491,501,511,521,531
%N a(n) = 10*n + 1.
%C Equals [1, 2, 3, ...] convolved with [1, 9, 0, 0, 0, ...]. - _Gary W. Adamson_, May 30 2009
%C Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=10, (i>1), A[i,i-1] = -1, and A[i,j]=0 otherwise. Then, for n>=2, a(n-1) = -coeff(charpoly(A,x),x^(n-1)). - _Milan Janjic_, Feb 21 2010
%C Positive integers with last decimal digit = 1. - _Wesley Ivan Hurt_, Jun 17 2015
%C Also the number of (not necessarily maximal) cliques in the 2n-crossed prism graph. - _Eric W. Weisstein_, Nov 29 2017
%H G. C. Greubel, <a href="/A017281/b017281.txt">Table of n, a(n) for n = 0..1000</a>
%H Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Janjic/janjic33.html">Hessenberg Matrices and Integer Sequences</a>, J. Int. Seq. 13 (2010) # 10.7.8.
%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/CrossedPrismGraph.html">Crossed 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+9*x)/(1-x)^2.
%F a(n) = 20*n - a(n-1) - 8, with a(0)=1. - _Vincenzo Librandi_, Nov 20 2010
%F a(n) = 2*a(n-1) - a(n-2), for n > 2. - _Wesley Ivan Hurt_, Jun 17 2015
%F E.g.f.: (1 + 10*x)*exp(x). - _G. C. Greubel_, Sep 18 2019
%p A017281:=n->10*n + 1; seq(A017281(n), n=0..80); # _Wesley Ivan Hurt_, Jan 29 2014
%t f[n_] := FromDigits[IntegerDigits[n^2, n + 1]]; Array[f, 60] (* _Robert G. Wilson v_, Apr 14 2009 *)
%t Range[1, 1000, 10] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%t (* From _Eric W. Weisstein_, Nov 29 2017: (Start) *)
%t Table[10n+1, {n, 0, 60}]
%t 10*Range[0, 60] + 1
%t LinearRecurrence[{2, -1}, {11, 21}, {0, 60}]
%t CoefficientList[Series[(1+9x)/(1-x)^2, {x, 0, 60}], x] (* End *)
%o (Haskell)
%o a017281 = (+ 1) . (* 10)
%o a017281_list = [1,11..] -- _Reinhard Zumkeller_, Apr 16 2012
%o (Magma) [10*n+1 : n in [0..60]]; // _Zaki Khandaker_, May 16 2015
%o (PARI) Vec((1+9*x)/(1-x)^2 + O(x^80)) \\ _Michel Marcus_, Jun 17 2015
%o (Sage) [10*n+1 for n in (0..60)] # _G. C. Greubel_, Sep 18 2019
%o (GAP) List([0..60], n-> 10*n+1 ); # _G. C. Greubel_, Sep 18 2019
%Y Cf. A093645 (column 1).
%Y Subsequence of A034709, together with A017293, A017329, A139222, A139245, A139249, A139264, A139279 and A139280.
%Y Cf. A048161, A154428.
%Y Cf. A005408, A016813, A016921, A017533, A161700, A128470, A158057, A161705, A161709, A161714.
%Y Cf. A030430 (primes).
%Y Cf. A272914, first comment. [_Bruno Berselli_, May 26 2016]
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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