

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
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OFFSET

2,1


COMMENTS

Sums of distinct powers of a. Numbers having only {0,1} in aary representation.


LINKS

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


FORMULA

T(a, n) = Sum{j>=1, [(n+2^(j1))/2^j] * ((a2)*a^(j1) + 1) }/(a1).
T(a, n) = Sum{j=1..n, ((a2)*a^A007814(j) + 1)/(a1) }.
G.f. of ath row: 1/(1x) * 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



