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Search: id:A104257
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| A104257 |
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Square array T(a,n) read by antidiagonals: replace 2^i with a^i in binary representation of n, where a,n>=2. |
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+0
16
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| 2, 3, 3, 4, 4, 4, 5, 5, 9, 5, 6, 6, 16, 10, 6, 7, 7, 25, 17, 12, 7, 8, 8, 36, 26, 20, 13, 8, 9, 9, 49, 37, 30, 21, 27, 9, 10, 10, 64, 50, 42, 31, 64, 28, 10, 11, 11, 81, 65, 56, 43, 125, 65, 30, 11, 12, 12, 100, 82, 72, 57, 216, 126, 68, 31, 12, 13, 13, 121, 101, 90, 73, 343
(list; table; graph; listen)
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OFFSET
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2,1
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COMMENT
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Sums of distinct powers of a. Numbers having only {0,1} in a-ary representation.
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FORMULA
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T(a, n) = Sum{j>=1, [(n+2^(j-1))/2^j] * ((a-2)*a^(j-1) + 1) }/(a-1).
T(a, n) = Sum{j=1..n, ((a-2)*a^A007814(j) + 1)/(a-1) }.
G.f. of a-th row: 1/(1-x) * Sum{k>=0, a^k*x^2^k/(1+x^2^k) }.
Recurrence: T(a, 2n) = aT(a, n), T(a, 2n+1) = aT(a, n) + 1, T(a, 0)=0.
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EXAMPLE
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2,3,4,5, 6, 7, 8, 9,
3,4,9,10,12,13,27,28,
4,5,16,17,20,21,64,65,
5,6,25,26,30,31,125,126,
6,7,36,37,42,43,216,217,
7,8,49,50,56,57,343,344,
8,9,64,65,72,73,512,513,
9,10,81,82,90,91,729,730,
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CROSSREFS
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Rows include (essentially) A005836, A000695, A033042, A033043, A033044, A033045, A033046, A033047, A033048, A033049, A033050, A033051, A033052.
Columns include A000290, A002522, A002378, A000578, A001093, A034262, A071568, A011379, A098547, A027444.
Main diagonal is A104258.
Sequence in context: A058889 A166724 A110862 this_sequence A048182 A029107 A063123
Adjacent sequences: A104254 A104255 A104256 this_sequence A104258 A104259 A104260
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Mar 05 2005
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