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A055235
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Sums of two powers of 3.
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5
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| 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)
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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EXAMPLE
| a(1) = 3^0+3^0, a(2) = 3^1+3^0, a(3) = 3^1+3^1,
a(4) = 3^2+3^0, a(5) = 3^2+3^1 = 12.
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MATHEMATICA
| mx = 10; Sort[Flatten[Table[3^x + 3^y, {y, 0, mx}, {x, 0, y}]]] (* From Vladimir Joseph Stephan Orlovsky, Apr 20 2011 *)
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 8 2011 *)
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PROG
| (PARI) for( n=0, 5, for(k=0, n, print1(3^n+3^k", ")))
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
| Cf. A052216.
Sequence in context: A045958 A076067 A065385 * A083887 A064374 A000885
Adjacent sequences: A055232 A055233 A055234 * A055236 A055237 A055238
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jun 22 2000
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EXTENSIONS
| Formula corrected by M. F. Hasler (maximilian.hasler(AT)gmail.com), Oct 08 2011
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