A249674 a(n) = 30*n.

0, 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780, 810, 840, 870, 900, 930, 960, 990, 1020, 1050, 1080, 1110, 1140, 1170, 1200, 1230, 1260, 1290, 1320, 1350, 1380, 1410, 1440

Offset: 0

Author

Kaylan Purisima, Nov 03 2014

Keywords

• nonn
• easy

Comments

Numbers divisible by 2, 3 and 5. - Robert Israel, Nov 19 2014

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

Examples

			a(7) = 7 * 30 = 210.
		

Links

• Iain Fox, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Bowling.
• Wikipedia, Ten-pin bowling.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A005843, A008585, A008587, A008588, A008592, A008597, A050519, A169823.

Programs

Magma

[30*n : n in [0..50]]; // Wesley Ivan Hurt, Nov 18 2014

Maple

A249674:=n->30*n: seq(A249674(n), n=0..50); # Wesley Ivan Hurt, Nov 18 2014

Mathematica

30*Range[0, 59] (* Alonso del Arte, Nov 18 2014 *)

PARI

vector(100,n,30*(n-1)) \\ Derek Orr, Nov 18 2014

PARI

first(n) = Vec(30*x/(x-1)^2 + O(x^n), -n) \\ Iain Fox, Mar 02 2018

Formula

G.f.: 30*x/(x-1)^2; a(n) = 2*a(n-1) - a(n-2). - Wesley Ivan Hurt, Nov 18 2014

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

From Elmo R. Oliveira, Apr 08 2025: (Start)

E.g.f.: 30*x*exp(x).

a(n) = A169823(n)/2. (End)