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A176653
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Triangle, read by rows, defined by T(n, m) = f(n-m)*f(n) - f(n-0)*f(0) + 1, where f(n) is 1 if n = 0 and Prime(n) otherwise.
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2
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1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 3, 4, 1, 1, 4, 5, 5, 4, 1, 1, 10, 9, 13, 9, 10, 1, 1, 10, 17, 19, 19, 17, 10, 1, 1, 16, 21, 37, 31, 37, 21, 16, 1, 1, 16, 29, 43, 55, 55, 43, 29, 16, 1, 1, 18, 29, 57, 63, 93, 63, 57, 29, 18, 1
(list;
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refs;
listen;
history;
text;
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OFFSET
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0,5
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COMMENTS
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Row sums are: {1, 2, 4, 6, 13, 20, 53, 94, 181, 288, 429, ...}.
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LINKS
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G. C. Greubel, Rows n = 0..100 of triangle, flattened
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FORMULA
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T(n, m) = f(n-m)*f(n) - f(n-0)*f(0) + 1, where f(n) is 1 if n = 0 and Prime(n) otherwise.
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 2, 1;
1, 2, 2, 1;
1, 4, 3, 4, 1;
1, 4, 5, 5, 4, 1;
1, 10, 9, 13, 9, 10, 1;
1, 10, 17, 19, 19, 17, 10, 1;
1, 16, 21, 37, 31, 37, 21, 16, 1;
1, 16, 29, 43, 55, 55, 43, 29, 16, 1;
1, 18, 29, 57, 63, 93, 63, 57, 29, 18, 1;
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MATHEMATICA
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f[n_]:= If[n==0, 1, Prime[n]]; T[n_, m_] = f[n-m]*f[m] - f[n]*f[0] + 1; Table[T[n, m], {n, 0, 12}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, May 07 2019 *)
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PROG
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(PARI)
{f(n) = if(n==0, 1, prime(n))};
{T(n, k) = f(n-k)*f(k) - f(k) + 1};
for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, May 07 2019
(Magma)
f:= func< n | n eq 0 select 1 else NthPrime(n) >;
[[f(n-k)*f(k) - f(n) + 1: k in [0..n]]: n in [0..12]]; // G. C. Greubel, May 07 2019
(Sage)
def f(n):
if (n==0): return 1
else: return nth_prime(n)
def T(n, k): return f(n-k)*f(k) - f(n) +1
[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, May 07 2019
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CROSSREFS
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Cf. A146985
Sequence in context: A331447 A352460 A342767 * A174842 A156074 A051287
Adjacent sequences: A176650 A176651 A176652 * A176654 A176655 A176656
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula, Apr 22 2010
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EXTENSIONS
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Edited by G. C. Greubel, May 07 2019
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STATUS
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approved
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