OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 2 + (3*n*n + 10*n + 11)*n/2. - Frank Ellermann, Mar 16 2002
a(n) = n^2(3n + 1)/2. - Ronnie B Kon (ronniekon(AT)yahoo.com), Jun 09 2006
G.f.: x*(2 + 6*x + x^2)/(1 - x)^4. - Colin Barker, Mar 27 2012
From Amiram Eldar, Jan 10 2023: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/3 + sqrt(3)*Pi + 9*log(3) - 18.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/6 - 2*sqrt(3)*Pi - 12*log(2) + 18. (End)
EXAMPLE
n=3 -> 3*(4+5+6)=45
MATHEMATICA
CoefficientList[Series[(2+6*x+x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 25 2012 *)
Table[(n^2*(1+3n))/2, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 14, 45, 104}, 40] (* Harvey P. Dale, Jan 04 2015 *)
PROG
(PARI) a(n)=n^2*(3*n+1)/2 \\ Charles R Greathouse IV, Dec 08 2011
(Magma) I:=[2, 14, 45, 104]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Apr 25 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
G. L. Honaker, Jr., Dec 15 1998
STATUS
approved