OFFSET
0,3
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,2,0,0,0,0,-1).
FORMULA
G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 6*x^4 + 3*x^5 + 4*x^6 + x^7 + 2*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)^2).
a(n) = 2*a(n-5) - a(n-10).
a(5*k+r) = (5+(-1)^r)*k + r, where r=0..4.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi*(1/(2*sqrt(2))-1/(3*sqrt(3))) + log(2)/6. - Amiram Eldar, Mar 30 2023
EXAMPLE
------------------------------------------------------------------------
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, ...
+ + + + + + + + + + + + + + + + + + +
0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 2, -2, 2, -2, 2, 3, -3, 3, -3, ...
------------------------------------------------------------------------
0, 1, 2, 3, 4, 6, 5, 8, 7, 10, 12, 9, 14, 11, 16, 18, 13, 20, 15, ...
------------------------------------------------------------------------
MATHEMATICA
Table[n + Floor[n/5] (-1)^Mod[n, 5], {n, 0, 80}]
PROG
(Sage) [n+floor(n/5)*(-1)^mod(n, 5) for n in (0..80)]
(Magma) [n+Floor(n/5)*(-1)^(n mod 5): n in [0..80]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 15 2015 - based on an idea by Paul Curtz.
STATUS
approved