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A058498
Number of solutions to c(1)t(1) + ... + c(n)t(n) = 0, where c(i) = +-1 for i>1, c(1) = t(1) = 1, t(i) = triangular numbers (A000217).
9
0, 0, 0, 1, 0, 1, 1, 2, 0, 6, 8, 13, 0, 33, 52, 105, 0, 310, 485, 874, 0, 2974, 5240, 9488, 0, 30418, 55715, 104730, 0, 352467, 642418, 1193879, 0, 4165910, 7762907, 14493951, 0, 50621491, 95133799, 179484713, 0, 637516130, 1202062094, 2273709847, 0, 8173584069
OFFSET
1,8
LINKS
Alois P. Heinz and Ray Chandler, Table of n, a(n) for n = 1..633 (first 280 terms from Alois P. Heinz)
FORMULA
a(n) = [x^(n*(n+1)/2)] Product_{k=1..n-1} (x^(k*(k+1)/2) + 1/x^(k*(k+1)/2)). - Ilya Gutkovskiy, Feb 01 2024
EXAMPLE
a(8) = 2 because there are two solutions: 1 - 3 + 6 + 10 + 15 - 21 + 28 - 36 = 1 - 3 - 6 + 10 - 15 + 21 + 28 - 36 = 0.
MAPLE
b:= proc(n, i) option remember; local m; m:= (2+(3+i)*i)*i/6;
`if`(n>m, 0, `if`(n=m, 1,
b(abs(n-i*(i+1)/2), i-1) +b(n+i*(i+1)/2, i-1)))
end:
a:= n-> `if`(irem(n, 4)=1, 0, b(n*(n+1)/2, n-1)):
seq(a(n), n=1..40); # Alois P. Heinz, Oct 31 2011
MATHEMATICA
b[n_, i_] := b[n, i] = With[{m = (2+(3+i)*i)*i/6}, If[n>m, 0, If[n == m, 1, b[Abs[n - i*(i+1)/2], i-1] + b[n + i*(i+1)/2, i-1]]]]; a[n_] := If[Mod[n, 4] == 1, 0, b[n*(n+1)/2, n-1]]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jan 30 2017, after Alois P. Heinz *)
CROSSREFS
Cf. A000217.
Sequence in context: A086777 A355978 A334349 * A358167 A348189 A372911
KEYWORD
nonn
AUTHOR
Naohiro Nomoto, Dec 20 2000
EXTENSIONS
More terms from Sascha Kurz, Oct 13 2001
More terms from Alois P. Heinz, Oct 31 2011
STATUS
approved