OFFSET
0,3
COMMENTS
Diagonal in array of n-gonal numbers A081422.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: (1 -4*x +11*x^2 -8*x^3)/(1-x)^5.
a(n) = (n + 1)*(2*n^2 - 3*n + 2)/2 = (n-1)*A005564(n+1) - n*A005564(n), where A005564(0..2) = 0, -1, 0. - Bruno Berselli, May 19 2015
E.g.f.: (2 + 5*x^2 + 2*x^3)*exp(x)/2. - G. C. Greubel, Aug 14 2019
MAPLE
a:= n-> (2*n^3-n^2-n+2)/2: seq(a(n), n=0..50); # Zerinvary Lajos, Sep 13 2006
MATHEMATICA
Table[(2n^3-n^2-n+2)/2, {n, 0, 40}] (* Harvey P. Dale, May 29 2012 *)
CoefficientList[Series[(1 - 4 x + 11 x^2 - 8 x^3) / (1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 08 2013 *)
PROG
(Magma) [(2*n^3-n^2-n+2)/2: n in [0..50]]; // Vincenzo Librandi, Aug 08 2013
(PARI) vector(40, n, n--; (2*n^3-n^2-n+2)/2) \\ G. C. Greubel, Aug 14 2019
(Sage) [(2*n^3-n^2-n+2)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019
(GAP) List([0..40]. n-> (2*n^3-n^2-n+2)/2); # G. C. Greubel, Aug 14 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 21 2003
STATUS
approved