A008598 Multiples of 16.

0, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, 432, 448, 464, 480, 496, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, 800, 816, 832

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

If X is an n-set and Y_i (i=1,2,3,4) mutually disjoint 2-subsets of X then a(n-6) is equal to the number of 5-subsets of X intersecting each Y_i (i=1,2,3,4). - Milan Janjic, Aug 26 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 328.
• Milan Janjic, Two Enumerative Functions.
• Tanya Khovanova, Recursive Sequences.
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
• Leo Tavares, Illustration: Square Block Star Frames
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008590, A008596, A008597, A014641, A174312, A185212.

Programs

Maple

A008598:=n->16*n; seq(A008598(n), n=0..100); # Wesley Ivan Hurt, Nov 13 2013

Mathematica

Range[0, 1000, 16] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
CoefficientList[Series[16 x / (x - 1)^2, {x, 0, 60}], x] (* Vincenzo Librandi Jun 10 2013 *)

PARI

a(n)=16*n \\ Charles R Greathouse IV, Sep 24 2015

Formula

a(n) = Sum_{k=1..8n} (i^k+1)*(i^(8n-k)+1), where i=sqrt(-1). - Bruno Berselli, Mar 19 2012

G.f.: 16*x/(x-1)^2. - Vincenzo Librandi, Jun 10 2013

a(n) = A014641(n) - A185212(n). - Leo Tavares, May 24 2022

From Elmo R. Oliveira, Apr 07 2025: (Start)

E.g.f.: 16*x*exp(x).

a(n) = 16*n = 2*A008590(n) = A174312(n)/2.

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