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A338431
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Row length of irregular triangle A337939.
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1
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1, 1, 1, 3, 3, 4, 6, 10, 8, 13, 15, 15, 21, 26, 21, 36, 36, 33, 45, 49, 42, 64, 66, 58, 72, 89, 71, 99, 105, 80, 120, 136, 105, 151, 137, 129, 171, 188, 147, 190, 210, 165, 231, 247, 184, 274, 276, 228, 288, 295
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OFFSET
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1,4
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LINKS
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FORMULA
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a(1) = 1, and for n >= 2, a(n) = Sum_{k=1..floor(n/2)} k = A000217(floor(n/2)) if b(n) := floor(n/2) - delta(n) = A219839(n) = 0, where delta(n) = A055034(n), and if b(n) > 0, i.e., n = n(j) = A111774(j), for j >= 1, then a(n) < A000217(floor(n/2)), determined by a(n) = A000217(delta(n)) + R(n), with R(n) = Sum_{k = delta(n)+1..floor(n/2)} (1 + degree(S(k-1, x) evaluated with C(n, x) = 0)), where the C polynomial coefficients are given in A187360.
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EXAMPLE
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n = 12: b(12) = 6 - 4 = 2 = A219839(12) > 0, hence A000217(4) = 10, R(4) = (1 + 2) + (1 + 1) = 5 from degree(S(4, x)/C(12,x) = 1*x^2) = 2 and degree(S(5, x)/C(12, x) = 2*x) = 1. Hence a(12) = 10 + 5 = 15.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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