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A290021
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a(0) = 1; for n > 0, a(n) = a(k) + a(m) where binomial(k + m + 2, 2) - m = n and binomial(k + m + 2, 2) is the smallest triangular number larger than or equal to m.
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1
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1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 4, 5, 5, 6, 5, 5, 5, 6, 6, 6, 6, 5, 5, 6, 7, 6, 7, 6, 5, 5, 6, 7, 7, 7, 7, 6, 5, 6, 6, 7, 7, 8, 7, 7, 6, 6, 6, 7, 7, 7, 8, 8, 7, 7, 7, 6, 5, 7, 8, 7, 8, 8, 8, 7, 8, 7, 5, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 7, 7, 8, 9, 8, 8, 8
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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a(0) = 1.
a(1) = a(0) + a(0) = 1 + 1 = 2.
a(2) = a(0) + a(1) = 1 + 2 = 3.
a(3) = a(1) + a(0) = 2 + 1 = 3.
a(4) = a(0) + a(2) = 1 + 3 = 4.
a(5) = a(1) + a(1) = 2 + 2 = 4.
a(6) = a(2) + a(0) = 3 + 1 = 4.
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PROG
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(PARI) a(n) = {if(n==0, return(1)); my(s = ceil((-3 + sqrt(8*n+1))/ 2), b = binomial(s+2, 2), k = b - n, m = s - k); a(k) + a(m)}
(PARI) a=vector(87); print1(a[u=1]=1); for (d=1, oo, for (n=1, d, print1(", "a[u++]=a[n]+a[d+1-n]); if (u==87, break (2)))) \\ Rémy Sigrist, Feb 12 2021
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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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