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 A104257 Square array T(a,n) read by antidiagonals: replace 2^i with a^i in binary representation of n, where a,n>=2. 17
 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; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Sums of distinct powers of a. Numbers having only {0,1} in a-ary representation. LINKS FORMULA 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. EXAMPLE 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, CROSSREFS 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: A226143 A166724 A110862 * A048182 A029107 A209727 Adjacent sequences:  A104254 A104255 A104256 * A104258 A104259 A104260 KEYWORD nonn,tabl AUTHOR Ralf Stephan, Mar 05 2005 STATUS approved

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