A008592 Multiples of 10: a(n) = 10 * n.

0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500, 510, 520, 530

Offset

0,2

Comments

Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01,1) and (11;0). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m X n 0-1 matrices in question is given by (n+2)*2^(m-1)+2*m*(n-1)-2 for m>1 and n>1. - Sergey Kitaev, Nov 12 2004

If Y is a 5-subset of an n-set X then, for n>=5, a(n-4) is the number of 3-subsets of X having at least two elements in common with Y. - Milan Janjic, Dec 08 2007

Complement of A067251; A168184(a(n)) = 0. [Reinhard Zumkeller, Nov 30 2009]

Where record values occur for the number of partitions of n into powers of 10: A179052(n) = A179051(a(n)). [Reinhard Zumkeller, Jun 27 2010]

Numbers ending in 0. - Wesley Ivan Hurt, Apr 10 2016

Links

Ivan Panchenko, Table of n, a(n) for n = 0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 322

Tanya Khovanova, Recursive Sequences

S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

From Vincenzo Librandi, Dec 24 2010: (Start)

G.f.: 10*x/(x-1)^2.

a(n) = 2*a(n-1)-a(n-2) for n>1. (End)

a(n) = Sum_{i=2n-2..2n+2} i. - Wesley Ivan Hurt, Apr 11 2016

E.g.f.: 10*x*exp(x). - Stefano Spezia, May 31 2021

Maple

A008592:=n->10*n: seq(A008592(n), n=0..100); # Wesley Ivan Hurt, Apr 10 2016

Mathematica

Range[0, 1000, 10] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)

Prog

(Haskell) a008592 = (10 *)  -- Reinhard Zumkeller, Jun 13 2015
(PARI) vector(50, n, n--; 10*n) \\ Michel Marcus, Feb 05 2016
(PARI) x='x+O('x^999); concat(0, Vec(10*x/(x-1)^2)) \\ Altug Alkan, Apr 11 2016
(PARI) apply( A008592(n)=10*n, [1..55]) \\ M. F. Hasler, Apr 23 2021
(Magma) [10*n : n in [0..100]]; // Wesley Ivan Hurt, Apr 10 2016

Crossrefs

Cf. A008590, A008591, A067251, A168184, A179051, A179052.

Sequence in context: A109597 A194233 A263172 * A158814 A359173 A118959

Adjacent sequences: A008589 A008590 A008591 * A008593 A008594 A008595

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved