A272914 -id:A272914 - cp's OEIS frontend

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

N. J. A. Sloane

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.
    · ·           · ·           · ·           · ·           * ·
    · ·           · ·           * ·           * ·           · ·
* * · · · ·   · · * · · ·   · · · · * ·   · · · · · ·   · · · · · *
* * · · · ·   · * · * · ·   · * · · · ·   * · · · * ·   * · · · · ·
    · ·           * ·           · *           · ·           · ·
    · ·           · ·           · ·           * ·           · *
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)

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).

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]

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

a017281 = (+ 1) . (* 10)
a017281_list = [1,11..]  -- Reinhard Zumkeller, Apr 16 2012

[10*n+1 : n in [0..60]]; // Zaki Khandaker, May 16 2015

A017281:=n->10*n + 1; seq(A017281(n), n=0..80); # Wesley Ivan Hurt, Jan 29 2014

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 *)

Vec((1+9*x)/(1-x)^2 + O(x^80)) \\ Michel Marcus, Jun 17 2015

[10*n+1 for n in (0..60)] # G. C. Greubel, Sep 18 2019

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

A017311 a(n) = (10*n + 3)^7.

Original entry on oeis.org

2187, 62748517, 3404825447, 42618442977, 271818611107, 1174711139837, 3938980639167, 11047398519097, 27136050989627, 60170087060757, 122987386542487, 235260548044817, 425927596977747, 736141813551277

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Cf. A272914, first comment. - Bruno Berselli, May 26 2016

[(10*n+3)^7: n in [0..20]]; // Vincenzo Librandi, Jul 31 2011

(10Range[0,20]+3)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{2187,62748517,3404825447,42618442977,271818611107,1174711139837,3938980639167,11047398519097},20] (* Harvey P. Dale, Oct 02 2017 *)

A017322 a(n) = (10*n + 4)^6.

Original entry on oeis.org

4096, 7529536, 191102976, 1544804416, 7256313856, 24794911296, 68719476736, 164206490176, 351298031616, 689869781056, 1265319018496, 2194972623936, 3635215077376, 5789336458816, 8916100448256

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

First bisection of A272914.

[(10*n+4)^6: n in [0..20]]; // Vincenzo Librandi, Aug 01 2011

A017333 a(n) = (10*n + 5)^5.

Original entry on oeis.org

3125, 759375, 9765625, 52521875, 184528125, 503284375, 1160290625, 2373046875, 4437053125, 7737809375, 12762815625, 20113571875, 30517578125, 44840334375, 64097340625, 89466096875, 122298103125, 164130859375, 216699865625, 281950621875, 362050628125, 459401384375

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A013663, A016757, A017329.

Cf. A272914 (first comment). [Bruno Berselli, May 26 2016]

[(10*n+5)^5: n in [0..25]]; // Vincenzo Librandi, Aug 02 2011

(10*Range[0,20]+5)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{3125,759375,9765625,52521875,184528125,503284375},20] (* Harvey P. Dale, May 15 2018 *)

G.f.: 3125*(x+1)*(x^4+236*x^3+1446*x^2+236*x+1)/(x-1)^6. - Colin Barker, Nov 14 2012
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^5.
a(n) = 5^5 * A016757(n).
Sum_{n>=0} 1/a(n) = 31*zeta(5)/100000.
Sum_{n>=0} (-1)^n/a(n) = Pi^5/960000. (End)

A017346 a(n) = (10*n + 6)^6.

Original entry on oeis.org

46656, 16777216, 308915776, 2176782336, 9474296896, 30840979456, 82653950016, 192699928576, 404567235136, 782757789696, 1418519112256, 2436396322816, 4001504141376, 6327518887936, 9685390482496

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Second bisection of A272914.

[(10*n+6)^6: n in [0..20]]; // Vincenzo Librandi, Aug 03 2011

A017355 a(n) = (10*n + 7)^3.

Original entry on oeis.org

343, 4913, 19683, 50653, 103823, 185193, 300763, 456533, 658503, 912673, 1225043, 1601613, 2048383, 2571353, 3176523, 3869893, 4657463, 5545233, 6539203, 7645373, 8869743, 10218313, 11697083

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A272914, first comment. [From Bruno Berselli, May 26 2016]

[(10*n+7)^3: n in [0..40]]; // Vincenzo Librandi, Aug 30 2011

(10 Range[0, 40] + 7)^3 (* or *) LinearRecurrence[{4, -6, 4, -1}, {343, 4913, 19683, 50653}, 40] (* Harvey P. Dale, Jun 11 2015 *)

a(0)=343, a(1)=4913, a(2)=19683, a(3)=50653; for n>3, a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Harvey P. Dale, Jun 11 2015

A017385 a(n) = (10*n + 9)^9.

Original entry on oeis.org

387420489, 322687697779, 14507145975869, 208728361158759, 1628413597910449, 8662995818654939, 35452087835576229, 119851595982618319, 350356403707485209, 913517247483640899, 2171893279442309389

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Cf. A272914, first comment. [From Bruno Berselli, May 26 2016]

[(10*n+9)^9: n in [0..20]]; // Vincenzo Librandi, Sep 01 2011

(10 Range[0, 20] + 9)^9 (* Harvey P. Dale, Sep 04 2011 *)

cp's OEIS Frontend

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

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A017311 a(n) = (10*n + 3)^7.

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A017322 a(n) = (10*n + 4)^6.

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A017333 a(n) = (10*n + 5)^5.

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A017346 a(n) = (10*n + 6)^6.

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A017355 a(n) = (10*n + 7)^3.

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A017385 a(n) = (10*n + 9)^9.

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