Revision History for A055372
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#32 by Alois P. Heinz at Tue Jan 21 09:04:13 EST 2020
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#31 by Alois P. Heinz at Tue Jan 21 09:03:10 EST 2020
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| CROSSREFS
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T(2n,n) gives A098402.
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| STATUS
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approved
editing
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#30 by Alois P. Heinz at Tue Jan 21 08:59:50 EST 2020
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#29 by Michel Marcus at Tue Jan 21 03:48:07 EST 2020
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#28 by Michel Marcus at Tue Jan 21 03:48:04 EST 2020
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| FORMULA
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a(n,k) = 2^(n-1)*C(n, k).), for n>0.
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| EXAMPLE
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Triangle begins:
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proposed
editing
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#27 by Michel Marcus at Tue Jan 21 02:59:20 EST 2020
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#26 by Michel Marcus at Tue Jan 21 02:57:51 EST 2020
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| DATA
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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
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proposed
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Discussion
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| Tue Jan 21
| 02:58
| Michel Marcus: added 2 more terms to complete last triangle row
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| 02:59
| Michel Marcus: I think a(n,k) = 2^(n-1)*C(n, k) that should have for n>0.
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#25 by Jon E. Schoenfield at Tue Jan 21 02:53:06 EST 2020
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#24 by Jon E. Schoenfield at Tue Jan 21 02:52:53 EST 2020
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| COMMENTS
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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
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| FORMULA
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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
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| EXAMPLE
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1;
1,, 1;
2,, 4,, 2;
4,, 12,, 12,, 4;
8,, 32,, 48,, 32,, 8;
...
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| STATUS
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approved
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#23 by N. J. A. Sloane at Sun Sep 08 19:59:10 EDT 2013
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| FORMULA
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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
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Discussion
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| Sun Sep 08
| 19:59
| OEIS Server: https://oeis.org/edit/global/1941
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