Revision History for A055372
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
| older changes
|
|
|
|
#32 by Alois P. Heinz at Tue Jan 21 09:04:13 EST 2020
|
|
|
|
#31 by Alois P. Heinz at Tue Jan 21 09:03:10 EST 2020
|
| CROSSREFS
|
T(2n,n) gives A098402.
|
| STATUS
|
approved
editing
|
|
|
|
#30 by Alois P. Heinz at Tue Jan 21 08:59:50 EST 2020
|
|
|
|
#29 by Michel Marcus at Tue Jan 21 03:48:07 EST 2020
|
|
|
|
#28 by Michel Marcus at Tue Jan 21 03:48:04 EST 2020
|
| FORMULA
|
a(n,k) = 2^(n-1)*C(n, k).), for n>0.
|
| EXAMPLE
|
Triangle begins:
|
| STATUS
|
proposed
editing
|
|
|
|
#27 by Michel Marcus at Tue Jan 21 02:59:20 EST 2020
|
|
|
|
#26 by Michel Marcus at Tue Jan 21 02:57:51 EST 2020
|
| DATA
|
1, 1, 1, 2, 4, 2, 4, 12, 12, 4, 8, 32, 48, 32, 8, 16, 80, 160, 160, 80, 16, 32, 192, 480, 640, 480, 192, 32, 64, 448, 1344, 2240, 2240, 1344, 448, 64, 128, 1024, 3584, 7168, 8960, 7168, 3584, 1024, 128, 256, 2304, 9216, 21504, 32256, 32256, 21504, 9216, 2304, 256
|
| STATUS
|
proposed
editing
|
|
|
Discussion
|
Tue Jan 21
| 02:58
| Michel Marcus: added 2 more terms to complete last triangle row
|
| 02:59
| Michel Marcus: I think a(n,k) = 2^(n-1)*C(n, k) that should have for n>0.
|
|
|
|
#25 by Jon E. Schoenfield at Tue Jan 21 02:53:06 EST 2020
|
|
|
|
#24 by Jon E. Schoenfield at Tue Jan 21 02:52:53 EST 2020
|
| COMMENTS
|
Triangle T(n,k), 0<= <= k<= <= n, read by rows, given by [1, 1, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - . - _Philippe Deléham (kolotoko(aT)lagoon.nc), _, Aug 10 2005
T(n,k) is the number of nonempty bit strings with n bits and exactly k 1's over all strings in the sequence. For example , T(2,1) =)=4 because we have: {( {(01)},{(10)},{(0),(1)},{(1),(0)}. - Geoffrey Critzer, Apr 06 2013
|
| FORMULA
|
a(n, ,k)=) = 2^(n-1)*C(n, k). G.f.: A(x, y)=(1-x-xy)/(1-2x-2xy).
G.f.: A(x, y)=(1-x-xy)/(1-2x-2xy).
Sum_{k, =0<=k<=..n} T(n,k)*x^k = A000007(n), A011782(n), A081294(n), A081341(n), A092811(n), A093143(n), A067419(n) for x = -1, 0, 1, 2, 3, 4, 5 respectively. - Philippe Deléham, Feb 05 2012
|
| EXAMPLE
|
1;
1,, 1;
2,, 4,, 2;
4,, 12,, 12,, 4;
8,, 32,, 48,, 32,, 8;
...
...
|
| STATUS
|
approved
editing
|
|
|
|
#23 by N. J. A. Sloane at Sun Sep 08 19:59:10 EDT 2013
|
| FORMULA
|
Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A011782(n), A081294(n), A081341(n), A092811(n), A093143(n), A067419(n) for x = -1, 0, 1, 2, 3, 4, 5 respectively. - . - _Philippe Deléham, _, Feb 05 2012
|
|
|
Discussion
|
Sun Sep 08
| 19:59
| OEIS Server: https://oeis.org/edit/global/1941
|
|
|
|
|