OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).
FORMULA
G.f.: x*(1 + 7*x + 4*x^2 + 3*x^3 + 4*x^4 - x^5 - x^6 - 2*x^7)/(1 - x^3)^3.
a(n) = numerator of n*(n+5)/6. - Altug Alkan, Apr 18 2018
From Peter Bala, Aug 06 2022: (Start)
a(n) is quasi-polynomial in n:
a(3*n) = (1/2)*n*(3*n+5) = A115067(n+1).
a(3*n+1) = (1/2)*(n+2)*(3*n+1) = A095794(n+1).
a(3*n+2) = (1/2)*(3*n+2)*(3*n+7) = A179436(n). (End)
Sum_{n>=1} 1/a(n) = 4*Pi/(15*sqrt(3)) + 87/50. - Amiram Eldar, Aug 11 2022
MATHEMATICA
CoefficientList[Series[x*(1+7*x+4*x^2+3*x^3+4*x^4-x^5-x^6-2*x^7)/(1-x^3)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 04 2014 *)
Numerator[25*Binomial[Range[0, 50]/5 +1, 2]/3] (* G. C. Greubel, Aug 05 2022 *)
PROG
(Magma) [Numerator(n*(n+5)/((n+2)*(n+3))): n in [0..50]]; // Vincenzo Librandi, Mar 04 2014
(PARI) a(n) = numerator(n*(n+5)/6); \\ Altug Alkan, Apr 18 2018
(SageMath) [numerator(n*(n+5)/6) for n in (0..50)] # G. C. Greubel, Aug 05 2022
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved