OFFSET
0,2
COMMENTS
Zero together with the partial partial sums of A195013.
Second bisection is 2, 9, 21, 38, 60, 87, 119, ...: A005476. - Omar E. Pol, Sep 25 2011
Number of pairs (x,y) with even x in {0,...,n}, odd y in {0,...,3n}, and x<y. - Clark Kimberling, Jul 02 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
G.f.: f(x)/g(x), where f(x) = 2*x + 3*x^2 and g(x) = (1+x)^2 * (1-x)^3. - Clark Kimberling, Jul 02 2012
a(n) = (10*n^2 + 18*n + 3 + (2*n - 3)*(-1)^n)/16. - Luce ETIENNE, Aug 11 2014
MATHEMATICA
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 2, 5, 9, 15}, 60] (* Harvey P. Dale, May 20 2019 *)
PROG
(Magma) [(10*n^2 + 18*n + 3 + (2*n - 3)*(-1)^n)/16 : n in [0..50]]; // Vincenzo Librandi, Oct 26 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 09 2011
STATUS
approved