A017281 a(n) = 10*n + 1.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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 maximal) cliques in the 2n-crossed prism graph. - Eric W. Weisstein, Nov 29 2017

From Martin Renner, May 28 2024: (Start)

Also number of squares in a grid cross with equally long arms and a width of two points (cf. A017113), e.g. for n = 2 there are nine squares of size 1 unit of area, four of size 2, two of size 5, four of size 8 and two of size 13, thus a total of 21 squares.

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The possible areas of the squares are given by ceiling(k^2/2) for 1 <= k <= 2*n+1, cf. A000982. In general, there are 4*n + 1 squares with one unit area to be found in the cross, cf. A016813, for n > 0 always four squares of even area and two squares of odd area > 1. (End)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Milan 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).

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]

Programs

GAP

List([0..60], n-> 10*n+1 ); # G. C. Greubel, Sep 18 2019

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

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 *)

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

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