A228571 The backwards antidiagonal sums of triangle A228570.

1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 5, 4, 7, 6, 10, 10, 14, 15, 20, 24, 30, 35, 45, 53, 69, 79, 104, 120, 157, 184, 236, 281, 356, 431, 540, 656, 821, 1001, 1252, 1525, 1908, 2328, 2909, 3557, 4434, 5436, 6762

Offset: 0

Author

Johannes W. Meijer, Aug 26 2013

Keywords

• nonn
• easy

Comments

The a(n) equal the backwards antidiagonal sums of triangle A228570.

Crossrefs

Cf. A228570, A102543, A192928, A001687.

Programs

Maple

f := x -> (1/((1-x^2-x^5)) + (1+x^2+x^5)/(1-x^4-x^10))/2 : seq(coeff(series(f(x), x, n+1), x, n), n=0..50);  # End first program
a := proc(n): (A001687(n+1) + x(n) + x(n-2) + x(n-5))/2 end: A001687 := proc(n) option remember: if n=0 then 0 elif n=1 then 1 elif n=2 then 0 elif n=3 then 1 elif n=4 then 0 else procname(n-2) + procname(n-5) fi: end: x := proc(n) local x: if n <0 then return(0) fi: if type(n, even) then A001687((n+2)/2) else 0 fi: end: seq(a(n), n=0..50); # End second program

Formula

a(n) = sum(A228570(n-k, n-2*k), k=0..floor(n/2)).

G.f.: (1/2)*(1/(1-x^2-x^5) + (1+x^2+x^5)/(1-x^4-x^10)).