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 A063993 Number of ways of writing n as an unordered sum of exactly 3 nonzero triangular numbers. 6
 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 1, 2, 0, 2, 2, 2, 1, 1, 2, 2, 2, 0, 3, 2, 2, 2, 2, 2, 1, 3, 1, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 3, 1, 2, 5, 1, 2, 1, 2, 5, 3, 3, 1, 4, 2, 3, 2, 2, 4, 4, 2, 1, 4, 3, 3, 3, 2, 4, 3, 3, 3, 4, 2, 1, 6, 1, 5, 3, 3, 5, 2, 2, 2, 5, 2, 5, 4, 2, 4, 5, 3, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS a(A002097(n)) = 0; a(A111638(n)) = 1; a(A064825(n)) = 2. - Reinhard Zumkeller, Jul 20 2012 LINKS T. D. Noe, Table of n, a(n) for n=0..5050 EXAMPLE 5 = 3 + 1 + 1, so a(5) = 1. MATHEMATICA a = Table[ n(n + 1)/2, {n, 1, 15} ]; b = {0}; c = Table[ 0, {100} ]; Do[ b = Append[ b, a[ [ i ] ] + a[ [ j ] ] + a[ [ k ] ] ], {k, 1, 15}, {j, 1, k}, {i, 1, j} ]; b = Delete[ b, 1 ]; b = Sort[ b ]; l = Length[ b ]; Do[ If[ b[ [ n ] ] < 100, c[ [ b[ [ n ] ] + 1 ] ]++ ], {n, 1, l} ]; c PROG (Haskell) a063993 n = length [() | let ts = takeWhile (< n) \$ tail a000217_list,                     x <- ts, y <- takeWhile (<= x) ts,                     let z = n - x - y, 0 < z, z <= y, a010054 z == 1] -- Reinhard Zumkeller, Jul 20 2012 CROSSREFS Cf. A053604, A008443, A002636, A064181. Cf. A000217, A010054. Sequence in context: A284154 A080028 A143223 * A115722 A115721 A279497 Adjacent sequences:  A063990 A063991 A063992 * A063994 A063995 A063996 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane, Sep 18 2001 EXTENSIONS More terms from Robert G. Wilson v, Sep 20 2001 STATUS approved

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