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
Keywords
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
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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
Comments