Revision History for A229756
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#13 by Ralf Stephan at Sat Oct 05 05:43:56 EDT 2013
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#12 by Joerg Arndt at Sat Oct 05 05:21:51 EDT 2013
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#11 by T. D. Noe at Wed Oct 02 13:20:15 EDT 2013
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#10 by T. D. Noe at Wed Oct 02 13:19:42 EDT 2013
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| COMMENTS
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Row n sums to C(2n, ,n) (A000984).
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| LINKS
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Andrew Woods, <a href="/A229756/b229756.txt">Rows n = 1..50 of triangle, flattened</a>
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| EXAMPLE
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.. 2
.. 2 4
.. 2 12 6
.. 2 32 28 8
.. 2 82 110 48 10
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| STATUS
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proposed
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Discussion
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| Wed Oct 02
| 13:20
| T. D. Noe: This probably related to other sequences. Please add something to the Cf. section.
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#9 by Andrew Woods at Sun Sep 29 08:21:28 EDT 2013
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#8 by Andrew Woods at Sun Sep 29 08:21:08 EDT 2013
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| LINKS
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Andrew Woods, <a href="/A229756/b229756.txt">Rows n = 1..50 of triangle, flattened</a>
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#7 by Andrew Woods at Sun Sep 29 08:13:28 EDT 2013
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#6 by Andrew Woods at Sun Sep 29 08:10:45 EDT 2013
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| FORMULA
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Let h(n,p,k) := sum(j=0..floor((n-p)/k), (-1)^j*C(p,j)*C(n-1-j*k,p-1)) with h(n,p,0) := 0, and let g(n,k) := 2*sum(i=1..n, h(n,i,k)*(h(n,i,k)+h(n,i+1,k))). Then T(n,k) = g(n,k)-g(n,k-1).
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| PROG
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(PARI)
h(n, p, k)=if(k==0, 0, sum(j=0, floor((n-p)/k), (-1)^j*binomial(p, j)*binomial(n-1-j*k, p-1)))
g(n, k)=2*sum(i=1, n, h(n, i, k)*(h(n, i, k)+h(n, i+1, k)))
T(n, k)=g(n, k)-g(n, k-1)
r(n)=vector(n, x, 2*T(n, x))
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Discussion
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| Sun Sep 29
| 08:13
| Andrew Woods: Yes. I just added it.
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#5 by Joerg Arndt at Sun Sep 29 04:56:16 EDT 2013
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#4 by Joerg Arndt at Sun Sep 29 04:56:12 EDT 2013
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| COMMENTS
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Row n sums to C(2n, n) (A000984).
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proposed
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