OFFSET
0,2
COMMENTS
a(n) is the number of triples (w,x,y) with all terms in {0,...,n} and 2|w-x|<max(w,x,y)-min(w,x,y). [Clark Kimberling, Jun 11 2012]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
FORMULA
a(n+1) - a(n) = A137928(n+1).
From Bruno Berselli, Nov 16 2011: (Start)
G.f.: 2*x*(1+x^2)/((1+x)*(1-x)^4).
a(n) = 2*A131941(n) = (2*n*(2*n^2+3*n+4)-3*(-1)^n+3)/12.
a(n) = -a(-n-1) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5). (End)
MATHEMATICA
CoefficientList[Series[2x (1+x^2)/((1+x)(1-x)^4), {x, 0, 50}], x] (* or *) LinearRecurrence[ {3, -2, -2, 3, -1}, {0, 2, 6, 16, 32}, 50] (* Harvey P. Dale, Jan 22 2023 *)
PROG
(Magma) [&+[(2*k+(-1)^k+1)*(n-k): k in [0..n]]: n in [0..42]]; // Bruno Berselli, Nov 16 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Dec 05 2009
STATUS
approved