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A245575 Number of ways of writing n as the sum of two quarter-squares (cf. A002620). 5
1, 2, 3, 2, 3, 2, 4, 2, 3, 2, 4, 2, 3, 4, 2, 2, 4, 2, 5, 0, 4, 4, 4, 0, 3, 4, 4, 2, 2, 4, 2, 4, 5, 0, 4, 0, 6, 4, 2, 2, 3, 2, 6, 2, 2, 4, 4, 0, 4, 2, 5, 4, 2, 2, 2, 4, 4, 2, 6, 0, 3, 4, 4, 0, 2, 6, 4, 2, 4, 2, 2, 0, 7, 4, 4, 0, 6, 0, 4, 2, 2, 6, 2, 2, 5, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(A182834(n)) mod 2 = 0; a(A007550(n)) mod 2 = 1;

a(A240952(n)) = n and a(A240952(m)) <> n for m < a(n);

a(A245585(n)) = 0.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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

Cf. A002620, A240025, A007550, A182834, A245585, A240952.

Sequence in context: A259940 A228829 A007978 * A096737 A304535 A241856

Adjacent sequences:  A245572 A245573 A245574 * A245576 A245577 A245578

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Aug 04 2014

STATUS

approved

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Last modified August 22 02:44 EDT 2019. Contains 326169 sequences. (Running on oeis4.)