OFFSET
0,3
COMMENTS
In fact ceiling(7n/2) is just as likely as floor(7n/2), so sequence could equally well be A047345. - Henry Bottomley, Jan 19 2001. a(1) is the only exception to this rule. - Dmitry Kamenetsky, Nov 03 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (corrected by Sean A. Irvine, Jan 18 2019)
Eric Weisstein's World of Mathematics, Dice.
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = floor(7*n/2) for n >= 2.
From Colin Barker, Jun 09 2013: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) for n >= 5.
G.f.: x - x^2 * (3*x^2-3*x-7) / ((x-1)^2*(x+1)). (End)
MAPLE
A030123:=n->if n = 1 then 1 else floor(7*n/2) end if: seq(A030123(n), n=0..100); # Wesley Ivan Hurt, Jan 23 2017, Corrected by Zhuorui He, Jan 28 2026
MATHEMATICA
CoefficientList[Series[x - x^2 * (3 x^2 - 3 x - 7)/((x - 1)^2 (x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 19 2013, Corrected by Zhuorui He, Jan 28 2026 *)
PROG
(Magma) I:=[0, 1, 7, 10, 14]; [n le 5 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Oct 19 2013, Corrected by Zhuorui He, Jan 28 2026
(PARI) a(n)=if(n==1, 1, 7*n\2) \\ Charles R Greathouse IV, Oct 07 2015, Corrected by Zhuorui He, Jan 28 2026
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(0) and a(1) added by Dmitry Kamenetsky, Nov 03 2017
STATUS
approved