A187989 Number of nondecreasing arrangements of 5 numbers x(i) in -(n+3)..(n+3) with the sum of sign(x(i))*2^|x(i)| zero.

36, 57, 82, 111, 144, 181, 222, 267, 316, 369, 426, 487, 552, 621, 694, 771, 852, 937, 1026, 1119, 1216, 1317, 1422, 1531, 1644, 1761, 1882, 2007, 2136, 2269, 2406, 2547, 2692, 2841, 2994, 3151, 3312, 3477, 3646, 3819, 3996, 4177, 4362, 4551, 4744, 4941

Offset: 1

Author

R. H. Hardin, Mar 18 2011

Keywords

• nonn

Examples

			Some solutions for n=3:
  -6  -4  -4  -6  -4  -3  -4  -3  -6  -3  -3  -6  -4  -5  -5  -1
  -1  -4  -4  -3  -1  -2  -3   0  -5  -3  -3  -1   1  -4  -2  -1
  -1  -4  -3   3   1  -2  -3   0   5  -2  -3   1   1   3  -2  -1
   2  -4   3   5   3   3   4   1   5   2  -3   5   2   3   3   1
   6   6   5   5   3   3   4   2   5   4   5   5   3   5   5   2
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..86 correcting the earlier _R. H. Hardin_ file at a(28).

Crossrefs

Row 5 of A187988.

Programs

Mathematica

AatE[n_, nminusfE_, E_] := AatE[n, nminusfE, E] = Module[{a, fEminus, fEplus, f0, resn}, If[E == 0, If[n == 0, 1, 0], a = 0; For[fEminus = 0, fEminus <= nminusfE, fEminus++, For[fEplus = 0, fEplus <= nminusfE - fEminus, fEplus++, f0 = nminusfE - fEminus - fEplus; resn = n - (2^E + 1)*fEminus + (2^E - 1)*fEplus; If[Abs[resn] <= (1 + 2^(E - 1))*f0, a = a + AatE[resn, f0, E - 1]]]]; a]];
T[n_, k_] := AatE[n, n, n + k - 2];
Table[T[5, k], {k, 1, 86}] (* Jean-François Alcover, Sep 18 2024, after R. J. Mathar in A187988 *)

Extensions

a(28) corrected by R. J. Mathar, May 09 2023