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 A017281 a(n) = 10*n + 1. 56
 1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 201, 211, 221, 231, 241, 251, 261, 271, 281, 291, 301, 311, 321, 331, 341, 351, 361, 371, 381, 391, 401, 411, 421, 431, 441, 451, 461, 471, 481, 491, 501, 511, 521, 531 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equals [1, 2, 3,...] convolved with [1, 9, 0, 0, 0,...]. - Gary W. Adamson, May 30 2009 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 Positive integers with last decimal digit = 1. - Wesley Ivan Hurt, Jun 17 2015 Also the number of (not necessarily maximum) cliques in the 2n-crossed prism graph. - Eric W. Weisstein, Nov 29 2017 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 M. Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8. Tanya Khovanova, Recursive Sequences Eric Weisstein's World of Mathematics, Clique Eric Weisstein's World of Mathematics, Crossed Prism Graph Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA G.f.: (1+9*x)/(1-x)^2. a(n) = 20*n - a(n-1) - 8, with a(0)=1. - Vincenzo Librandi, Nov 20 2010 a(n) = 2*a(n-1) - a(n-2), for n > 2. - Wesley Ivan Hurt, Jun 17 2015 E.g.f.: (1 + 10*x)*exp(x). - G. C. Greubel, Sep 18 2019 MAPLE A017281:=n->10*n + 1; seq(A017281(n), n=0..80); # Wesley Ivan Hurt, Jan 29 2014 MATHEMATICA f[n_] := FromDigits[IntegerDigits[n^2, n + 1]]; Array[f, 60] (* Robert G. Wilson v, Apr 14 2009 *) Range[1, 1000, 10] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *) From Eric W. Weisstein, Nov 29 2017: (Start) Table[10n+1, {n, 0, 60}] 10*Range[0, 60] + 1 LinearRecurrence[{2, -1}, {11, 21}, {0, 60}] CoefficientList[Series[(1+9x)/(1-x)^2, {x, 0, 60}], x] (End) PROG (Haskell) a017281 = (+ 1) . (* 10) a017281_list = [1, 11..]  -- Reinhard Zumkeller, Apr 16 2012 (MAGMA) [10*n+1 : n in [0..60]]; // Zaki Khandaker, May 16 2015 (PARI) Vec((1+9*x)/(1-x)^2 + O(x^80)) \\ Michel Marcus, Jun 17 2015 (Sage) [10*n+1 for n in (0..60)] # G. C. Greubel, Sep 18 2019 (GAP) List([0..60], n-> 10*n+1 ); # G. C. Greubel, Sep 18 2019 CROSSREFS Cf. A093645 (column 1). Subsequence of A034709, together with A017293, A017329, A139222, A139245, A139249, A139264, A139279 and A139280. Cf. A048161, A154428. Cf. A005408, A016813, A016921, A017533, A161700, A128470, A158057, A161705, A161709, A161714. Cf. A030430 (primes). Cf. A272914, first comment. [Bruno Berselli, May 26 2016] Sequence in context: A123849 A108812 A216100 * A061589 A110402 A081927 Adjacent sequences:  A017278 A017279 A017280 * A017282 A017283 A017284 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 20 12:33 EDT 2019. Contains 328257 sequences. (Running on oeis4.)