|
| |
|
|
A091913
|
|
Matrix defined by: for n <= k, a(n,k) = 0; for n > k, a(n,k) = C(n,k) * (2^(n-k) - 1) - read by rows.
|
|
1
| |
|
|
0, 1, 3, 2, 7, 9, 3, 15, 28, 18, 4, 31, 75, 70, 30, 5, 63, 186, 225, 140, 45, 6, 127, 441, 651, 525, 245, 63, 7, 255, 1016, 1764, 1736, 1050, 392, 84, 8, 511, 2295, 4572, 5292, 3906, 1890, 588, 108, 9, 1023, 5110, 11475, 15240, 13230, 7812, 3150, 840, 135, 10, 2047
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Rows: Sum of the n-th row = A001047(n); Sum of the n-th row excluding column 0 = A028243(n+1). Columns: a(n,0) = A000225(n); a(n,1) = A058877(n). Diagonals: a(n,n-2) = A045943(n-1). Also note that the sums of the antidiagonals = A006684.
|
|
|
FORMULA
| For n <= k, a(n, k) = 0; for n > k, a(n, k) = C(n, k) * (2^(n-k) - 1). For n > k, a(n, k) = Sum [C(n,k) * C(n-k, m), {m=1 to n-k}]. [Formula corrected Aug 22 2006]
The triangle (1; 3,2; 7,9,3;...) = A007318^2 - A007318, then delete the right border of zeros. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 16 2007
|
|
|
EXAMPLE
| {0}; {1}; {3,2}; {7,9,3}; {15,28,18,4}; {31,75,70,30,5}; {63,186,225,140,45,6}
a(5,3) = 30 because C(5,3) = 10, 2^(5-3) - 1 = 3 and 10 * 3 = 30.
|
|
|
CROSSREFS
| Cf. A007318, A038207.
Cf. A007318.
Sequence in context: A054170 A106167 A194473 * A192789 A026136 A026172
Adjacent sequences: A091910 A091911 A091912 * A091914 A091915 A091916
|
|
|
KEYWORD
| easy,nonn,tabl
|
|
|
AUTHOR
| Ross La Haye (rlahaye(AT)new.rr.com), Mar 10 2004
|
|
|
EXTENSIONS
| More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
|
| |
|
|
