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A104746
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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.
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2
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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; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row 2 of the array = binomial transform for 1, 2, 3...(A001787). Row 3 of the array = binomial transform for 1, 3, 5...(A000337). Row 4 of the array = binomial transform for 1, 4, 7...(A027992). Row 5 of the array = binomial transform for 1, 5, 9...(A059823). Generally, row n of the array = binomial transform for 1, n, (2n - 1)... The operator sequence A000337 (1, 5, 17, 49, 129...) = row 3 of the array, starting with 1. Row sums = A104747: 1, 4, 12, 33, 87, 222, 550...
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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...
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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
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CROSSREFS
| Cf. A104747, A001787, A000337, A027992, A059823.
Sequence in context: A081521 A086273 A054143 * A193969 A169838 A081255
Adjacent sequences: A104743 A104744 A104745 * A104747 A104748 A104749
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 23 2005
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EXTENSIONS
| Terms corrected by R. J. Mathar, Oct 30 2011
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