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

0,10

Comments

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

Links

Table of n, a(n) for n=0..50.

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)).

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

Crossrefs

Cf. A228570, A102543, A192928, A001687.

Sequence in context: A369985 A295630 A029147 * A224908 A029097 A210955

Adjacent sequences: A228568 A228569 A228570 * A228572 A228573 A228574

Keyword

nonn,easy

Author

Johannes W. Meijer, Aug 26 2013

Status

approved