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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

Table of n, a(n) for n=2..74.

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 A300293 A316388

Adjacent sequences:  A104254 A104255 A104256 * A104258 A104259 A104260

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Mar 05 2005

STATUS

approved

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Last modified February 26 21:58 EST 2020. Contains 332295 sequences. (Running on oeis4.)