OFFSET
0,2
COMMENTS
All terms are multiples of 3.
REFERENCES
Jolley, Summation of Series, Dover (1961), eq (43) page 8.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = ((4n^2 - 1)*(2n + 3)*(2n + 5) + 15)/ 8 = Sum_{i=1..n} (2i - 1)*(2i + 1)*(2i + 3).
G.f. -3*x*(5 + 15*x - 5*x^2 + x^3) / (x-1)^5 .
a(n) = 2 n^4 + 8 n^3 + 7 n^2 - 2 n. - Harvey P. Dale, Mar 14 2015, corrected by Eric Rowland, Aug 15 2017
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 15, 120, 435, 1128}, 40] (* or *) Accumulate[ Join[{0}, Times@@@Partition[Range[1, 111, 2], 3, 1]]] (* or *) Table[2n^4-5n^2+3, {n, 40}](* Harvey P. Dale, Mar 14 2015 *)
PROG
(Magma) [((4*n^2-1)*(2*n+3)*(2*n+5)+15)/ 8 : n in [0..30]]; // Vincenzo Librandi, Oct 05 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Oct 03 2011
STATUS
approved