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A063890 Number of solutions to +- 1 +- 2 +- 3 +- ... +- n = n. 1
1, 1, 0, 0, 2, 3, 0, 0, 12, 21, 0, 0, 113, 202, 0, 0, 1218, 2241, 0, 0, 14326, 26776, 0, 0, 177714, 335607, 0, 0, 2287975, 4353975, 0, 0, 30282850, 57965473, 0, 0, 409476546, 787414730, 0, 0, 5631955466, 10870618388, 0, 0, 78545902971 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Ray Chandler, Table of n, a(n) for n = 0..1000

EXAMPLE

a(8) = 12 because 8 = 1+2+3+4+5-6+7-8 = -1+2+3+4-5+6+7-8 = 1-2+3-4+5+6+7-8 = -1-2-3+4+5+6+7-8 = -1+2+3+4+5-6-7+8 = 1-2+3+4-5+6-7+8 = 1+2-3-4+5+6-7+8 = -1-2+3-4+5+6-7+8 = 1+2-3+4-5-6+7+8 = -1-2+3+4-5-6+7+8 = -1+2-3-4+5-6+7+8 = 1-2-3-4-5+6+7+8.

MATHEMATICA

f[n_, s_] := f[n, s]=Which[n==0, If[s==0, 1, 0], Abs[s]>(n*(n+1))/2, 0, True, f[n-1, s-n]+f[n-1, s+n]]; a[n_] := f[n, n]

nmax = 44; d = {1}; a1 = {1};

Do[

  d = PadLeft[d, Length[d] + 2 n] + PadRight[d, Length[d] + 2 n];

  i = Ceiling[Length[d]/2] + n;

  AppendTo[a1, If[i > Length[d], 0, d[[i]]]];

  , {n, nmax}];

a1 (* Ray Chandler, Mar 25 2014 *)

CROSSREFS

Cf. A025591, A063865-A063867.

Sequence in context: A011311 A240658 A342315 * A156439 A087734 A073644

Adjacent sequences:  A063887 A063888 A063889 * A063891 A063892 A063893

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Aug 28 2001

EXTENSIONS

More terms from Dean Hickerson, Aug 30, 2001

STATUS

approved

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Last modified May 15 17:50 EDT 2021. Contains 343920 sequences. (Running on oeis4.)