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A153046
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Multiplicative encoding of Losanitsch's triangle (A034851)
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1
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..7.
Eric Weisstein's World of Mathematics, Losanitsch's Triangle.
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FORMULA
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prime(k + 1)^(a(n, k)), where prime(k + 1) is the (k + 1)st prime number (A000040), n is a row number in Losanitsch's triangle and k is a column number (in both the numbering starts from 0) and a(n, k) is the value look-up function for Losanitsch's triangle.
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EXAMPLE
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The fourth row of Losanitsch's triangle is 1, 2, 4, 2, 1 and the first five primes are 2, 3, 5, 7, 11, therefore the fourth term is 2^1 * 3^2 * 5^4 * 7^2 * 11^1 = 6063750.
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MATHEMATICA
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a[n_, 0] := 1; a[n_, n_] := 1; a[n_, k_] := a[n, k] = a[n - 1, k - 1] + a[n - 1, k] - Binomial[n/2 - 1, (k - 1)/2]Mod[k, 2]Mod[n - 1, 2]; (* The above comes from Weisstein's Mathematica notebook *) multEncLoz[n_] := Times @@ Table[Prime[k + 1]^a[n, k], {k, 0, n}]; Table[multEncLoz[n], {n, 0, 7}]
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CROSSREFS
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Cf. A007188 (multiplicative encoding of Pascal's triangle).
Sequence in context: A227105 A127295 A352127 * A088260 A232171 A231816
Adjacent sequences: A153043 A153044 A153045 * A153047 A153048 A153049
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KEYWORD
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nonn
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AUTHOR
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Alonso del Arte, Dec 17 2008
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STATUS
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approved
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