A249674 - OEIS

%I #48 Sep 08 2022 08:46:10

%S 0,30,60,90,120,150,180,210,240,270,300,330,360,390,420,450,480,510,

%T 540,570,600,630,660,690,720,750,780,810,840,870,900,930,960,990,1020,

%U 1050,1080,1110,1140,1170,1200,1230,1260,1290,1320,1350,1380,1410,1440

%N a(n) = 30*n.

%C Numbers divisible by 2, 3 and 5. - _Robert Israel_, Nov 19 2014

%C a(n) is the maximum score of a 10-pin n-frame bowling game and the maximum score of an n-pin 10-frame bowling game, given the rules: a strike is worth the number of pins in each frame plus the number of pins knocked down by the next two balls (except in the last frame), a spare is worth the number of pins in each frame plus the number of pins knocked down by the next ball (except in the last frame), and if a strike or spare is earned in the last frame then the player must continue to throw balls until they have thrown 3 balls in the last frame. - _Iain Fox_, Mar 02 2018

%H Iain Fox, <a href="/A249674/b249674.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Bowling.html">Bowling</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Ten-pin_bowling">Ten-pin bowling</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: 30*x/(x-1)^2; a(n) = 2*a(n-1) - a(n-2). - _Wesley Ivan Hurt_, Nov 18 2014

%F a(n) = 2*A008597(n) = 3*A008592(n) = 5*A008588(n) = 6*A008587(n) = 10*A008585(n) = 15*A005843(n). - _Omar E. Pol_, Nov 24 2014

%e a(7) = 7 * 30 = 210.

%p A249674:=n->30*n: seq(A249674(n), n=0..50); # _Wesley Ivan Hurt_, Nov 18 2014

%t 30*Range[0, 59] (* _Alonso del Arte_, Nov 18 2014 *)

%o (Magma) [30*n : n in [0..50]]; // _Wesley Ivan Hurt_, Nov 18 2014

%o (PARI) vector(100,n,30*(n-1)) \\ _Derek Orr_, Nov 18 2014

%o (PARI) first(n) = Vec(30*x/(x-1)^2 + O(x^n), -n) \\ _Iain Fox_, Mar 02 2018

%Y Cf. A008585, A008592, A050519.

%K nonn,easy

%O 0,2

%A _Kaylan Purisima_, Nov 03 2014