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A055235
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Sums of two powers of 3.
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13
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2, 4, 6, 10, 12, 18, 28, 30, 36, 54, 82, 84, 90, 108, 162, 244, 246, 252, 270, 324, 486, 730, 732, 738, 756, 810, 972, 1458, 2188, 2190, 2196, 2214, 2268, 2430, 2916, 4374, 6562, 6564, 6570, 6588, 6642, 6804, 7290, 8748, 13122, 19684, 19686, 19692, 19710
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n+1) = 3^(n-trinv(n)*(trinv(n)+1)/2)+3^trinv(n), where trinv(n) = floor((sqrt(1+8*n)-1)/2) = A003056(n) and n-trinv(n)*(trinv(n)+1)/2 = A002262(n). [corrected by M. F. Hasler, Oct 08 2011]
Regarded as a triangle, T(n, k) = 3^n + 3^k, because 3^n + 3^n < 3^(n+1) + 3^0 for all n > 0.
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MATHEMATICA
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f[n_] := Block[{t = Floor[(Sqrt[1 + 8 (n - 1)] - 1)/2]}, 3^(n - 1 - t*(t + 1)/2) + 3^t]; Array[f, 49] (* Robert G. Wilson v, Oct 08 2011 *)
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PROG
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(PARI) for( n=0, 5, for(k=0, n, print1(3^n+3^k", ")))
(PARI) A055235(n)={ my( t=(sqrtint(8*n-7)-1)\2); 3^t+3^(n-1-t*(t+1)/2) } \\ M. F. Hasler, Oct 08 2011
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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