OFFSET
1,2
COMMENTS
Equals binomial transform of [1, 7, 15, 9, 0, 0, 0, ...] where (1, 7, 15, 9) = row 3 of triangle A038763. - Gary W. Adamson, Jul 19 2008
Equals convolution square of 1, 4, 7, 10, 13, 16, 19, ..., A016777. - Gary W. Adamson, Jul 28 2009
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (3*n^3 - 3*n^2 + 2*n)/2.
G.f.: x*(2*x+1)^2 / ( (x-1)^4 ).
MATHEMATICA
CoefficientList[Series[x (2x+1)^2/((x-1)^4), {x, 0, 50}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 1, 8, 30}, 50] (* Harvey P. Dale, Mar 18 2023 *)
PROG
(Magma) [(3*n^3-3*n^2+2*n)/2: n in [1..50] ]; // Vincenzo Librandi, Aug 02 2011
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
James A. Record (james.record(AT)gmail.com), Nov 07 2004
STATUS
approved