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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 (list; graph; refs; listen; history; text; internal format)
 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) 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 A003076 Adjacent sequences: A058495 A058496 A058497 * A058499 A058500 A058501 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

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Last modified February 7 02:40 EST 2023. Contains 360111 sequences. (Running on oeis4.)