OFFSET
0,2
COMMENTS
a(n) is also the number of times n appears in the triangle A338796, or equivalently, the number of positive integer solutions of the equation A338796(x, y) = n for y <= x. - Stefano Spezia, Mar 03 2022
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
FORMULA
EXAMPLE
a(10) = #{9+1, 6+4, 4+6, 1+9} = 4;
a(11) = #{9+2, 2+9} = 2;
a(12) = #{12+0, 6+6, 0+12} = 3;
a(13) = #{12+1, 9+4, 4+9, 1+12} = 4;
a(14) = #{6+1, 1+6} = 2;
a(15) = #{9+6, 6+9} = 2;
a(16) = #{16+0, 12+4, 4+12, 0+16} = 4;
a(17) = #{16+1, 1+16} = 2;
a(18) = #{16+2, 12+6, 9+9, 6+12, 2+16} = 5;
a(19) = #{} = 0;
a(20) = #{20+0, 16+4, 4+16, 0+20} = 4.
MATHEMATICA
qsQ[n_] := qsQ[n] = With[{s = Sqrt[n]}, Which[IntegerQ[s], True, n == Floor[s] (Floor[s]+1), True, True, False]]; a[n_] := Count[Range[0, n], k_ /; qsQ[k] && qsQ[n-k]]; Array[a, 100, 0] (* Jean-François Alcover, May 08 2017 *) (* or *)
u[{x_, y_}] := 2-Boole[x==y]; a[n_] := Total[u /@ IntegerPartitions[n, {2}, Floor[Range[1 + 2 Sqrt@ n]^2/4]]]; Array[a, 100, 0] (* Giovanni Resta, May 08 2017 *)
PROG
(Haskell)
a245575 n = a245575_list !! n
a245575_list = f 0 [] $ tail a002620_list where
f u vs ws'@(w:ws)
| u < w = (sum $ map (a240025 . (u -)) vs) : f (u + 1) vs ws'
| otherwise = f u (w : vs) ws
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Aug 04 2014
STATUS
approved