OFFSET
0,3
COMMENTS
Binomial transform of the sequence 1, 0, 3, 3, 0, 0, 0, ... .
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 1+A027480(n-1) for n>=1. - R. J. Mathar, Mar 28 2009
G.f.: 1-x*(-1-3*x^2+x^3) / (x-1)^4 . - R. J. Mathar, Nov 05 2011
E.g.f.: exp(x)*(1 + x^3/2 + 3*x^2/2). - Nikolaos Pantelidis, Feb 13 2023
EXAMPLE
a(4) = 31 = sum of row 4 terms of triangle A158841: (13 + 9 + 6 + 3).
MAPLE
A158842 := proc(n)
1+n*(n+1)*(n-1)/2 ;
end proc:
seq(A158842(n), n=0..30) ; # R. J. Mathar, Nov 05 2011
MATHEMATICA
Table[1 + n*(n + 1)*(n - 1)/2, {n, 40}] (* and *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 13, 31}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2012 *)
PROG
(Magma) [1+ n*(n+1)*(n-1)/2: n in [1..50]]; // Vincenzo Librandi, Nov 16 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson & Roger L. Bagula, Mar 28 2009
EXTENSIONS
a(0)=1 prepended by Andrew Howroyd, Feb 14 2023
STATUS
approved