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A118181
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Row sums of triangle A118180: a(n) = Sum_{k=0..n} (3^k)^(n-k) for n>=0.
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3
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1, 2, 5, 20, 137, 1622, 33293, 1182440, 72811793, 7757988842, 1433154521621, 458101483131260, 253879024041595289, 243453910296759945662, 404765167247068325944349, 1164432505878183620543030480
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OFFSET
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0,2
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COMMENTS
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Also equals column 0 of the matrix square of triangle A118180, where [A118180^2](n,k) = a(n-k)*(3^k)^(n-k) for n>=k>=0.
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LINKS
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FORMULA
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G.f.: A(x) = Sum_{n>=0} x^n/(1-3^n*x).
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EXAMPLE
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A(x) = 1/(1-x) + x/(1-3x) + x^2/(1-9x) + x^3/(1-27x) + ...
= 1 + 2*x + 5*x^2 + 20*x^3 + 137*x^4 + 1622*x^5 + 33293*x^6 +...
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MAPLE
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seq( add(3^(k*(n-k)), k=0..n), n=0..30); # modified by G. C. Greubel, Jun 29 2021
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MATHEMATICA
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Table[Sum[3^(k*(n-k)), {k, 0, n}], {n, 0, 30}] (* G. C. Greubel, Jun 29 2021 *)
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PROG
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(PARI) a(n)=sum(k=0, n, (3^k)^(n-k) );
(Magma) [(&+[3^(k*(n-k)): k in [0..n]]): n in [0..30]]; // G. C. Greubel, Jun 29 2021
(Sage) [sum(3^(k*(n-k)) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jun 29 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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