OFFSET
1,1
REFERENCES
L. B. W. Jolley, Summation of Series, Dover Publications, 1961, p. 12
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
Sum_{i=1..n} a(i) = n*(n+1)*(5n+7)/3 = 2*A162148(n).
a(n) = 2*A147875(n+1).
From G. C. Greubel, Aug 23 2017: (Start)
G.f.: 2*x*(x + 4)/(1 - x)^3.
E.g.f.: x*(5*x + 8)*exp(x). (End)
Sum_{n>=1} 1/a(n) = 5/9 + sqrt(1-2/sqrt(5))*Pi/6 + log(phi)*sqrt(5)/6 - 5*log(5)/12, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 21 2022
EXAMPLE
a(24) = 5*24^2 + 3*24 = 2880 + 72 = 2952.
MAPLE
a:=n->5*n^2+3*n: seq(a(n), n=1..55); # Emeric Deutsch, Apr 17 2007
MATHEMATICA
Table[n*(5*n + 3), {n, 1, 50}] (* G. C. Greubel, Aug 23 2017 *)
PROG
(PARI) a(n)=5*n^2+3*n \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 22 2006
EXTENSIONS
More terms from Emeric Deutsch, Apr 17 2007
STATUS
approved