OFFSET
0,2
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
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).
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)
EXAMPLE
a(7) = 7 * 30 = 210.
MAPLE
MATHEMATICA
30*Range[0, 59] (* Alonso del Arte, Nov 18 2014 *)
PROG
(Magma) [30*n : n in [0..50]]; // Wesley Ivan Hurt, 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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kaylan Purisima, Nov 03 2014
STATUS
approved