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A104746 Array T(n,k) read by antidiagonals: T(1,k) = 2^k-1 and recursively T(n,k) = T(n-1,k)+A000337(k-1), n,k >=1. 2
1, 1, 3, 1, 4, 7, 1, 5, 12, 15, 1, 6, 17, 32, 31, 1, 7, 22, 49, 80, 63, 1, 8, 27, 66, 129, 192, 127, 1, 9, 32, 83, 178, 321, 448, 255, 1, 10, 37, 100, 227, 450, 769, 1024, 511, 1, 11, 42, 117, 276, 579, 1090, 1793, 2304, 1023, 1, 12, 47, 134, 325, 708, 1411, 2562, 4097, 5120, 2047, 1, 13, 52, 151, 374, 837 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Generally, row n of the array is the binomial transform for 0, 1, n, 2n - 1, 3n-2, 4n-3, ...

LINKS

Table of n, a(n) for n=1..72.

FORMULA

T(2,k) = A001787(k), binomial transform of 0, 1, 2, 3, 4, 5, 6,...

T(3,k) = A000337(k), binomial transform of 0, 1, 3, 5, 7, 9, 11,...

T(4,k) = A027992(k-1), binomial transform of 0, 1, 4, 7, 10, 13, 16, 19, 22, 25,...

T(5,k) = binomial transform of 0, 1, 5, 9, 13, 17, 21, 25, 29

EXAMPLE

To the first row, add the terms 0, 1, 5, 17, 49, 129...as indicated:

1, 3, 7, 15, 31, 63...

0, 1, 5, 17, 49, 129... (getting row 2 of the array:

1, 4 12, 32, 80, 192...(= A001787, binomial transform for 1,2,3...)

Repeat the operation, getting the following array T(n,k):

1, 3, 7, 15, 31, 63...

1, 4, 12, 32, 80, 192...

1, 5, 17, 49, 129, 321...

1, 6, 22, 66, 178, 450...

MAPLE

A000337 := proc(n)

        1+(n-1)*2^n ;

end proc:

A104746 := proc(n, k)

        option remember;

        if n=  1 then

                2^k-1 ;

        else

                procname(n-1, k)+A000337(k-1) ;

        end if;

end proc:

for d from 1 to 12 do

        for k from 1 to d do

                n := d-k+1 ;

                printf("%d, ", A104746(n, k)) ;

        end do:

end do; # R. J. Mathar, Oct 30 2011

CROSSREFS

Cf. A104747 (antidiagonal sums), A001787, A000337, A027992, A059823.

Sequence in context: A210218 A086273 A054143 * A208339 A328463 A185722

Adjacent sequences:  A104743 A104744 A104745 * A104747 A104748 A104749

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Mar 23 2005

EXTENSIONS

Terms corrected by R. J. Mathar, Oct 30 2011

STATUS

approved

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)