Revision History for A213387
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#48 by Michael De Vlieger at Mon Feb 19 12:10:37 EST 2024
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#47 by Joerg Arndt at Mon Feb 19 11:49:25 EST 2024
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#46 by Joerg Arndt at Mon Feb 19 11:49:12 EST 2024
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Discussion
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| Mon Feb 19
| 11:49
| Joerg Arndt: yes it is
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#45 by Joerg Arndt at Mon Feb 19 11:48:46 EST 2024
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| FORMULA
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G.f.: -.: x^2*(2+x) / ( (1-2*x-1)*(x-1-x)^2 ). - R. J. Mathar, Jun 29 2012
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| STATUS
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proposed
editing
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#44 by Jon E. Schoenfield at Mon Feb 19 11:27:23 EST 2024
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#43 by Jon E. Schoenfield at Mon Feb 19 11:26:43 EST 2024
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| FORMULA
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G.f.: -x^2*(2+x) / () / ( (2*x-1)*(x-1)^2 ). - R. J. Mathar, Jun 29 2012
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Discussion
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| Mon Feb 19
| 11:27
| Jon E. Schoenfield: Is this attempted correction to the g.f. correct?
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#42 by Jon E. Schoenfield at Mon Feb 19 11:25:57 EST 2024
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| FORMULA
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a(1)=0, a(2)=2, a(3)=9, a(n)=) = 4*a(n-1)-) - 5*a(n-2)+) + 2*a(n-3); a(1)=0, a(2)=2, a(3). - _)=9. - _Harvey P. Dale_, Sep 28 2012
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| EXAMPLE
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For n=5, m(5,1)=16, m(4,2)=15, m(3,3)=11, m(2,4)=11, m(1,5)=10 gives the sum 63= = 2*A000295(4)+) + A095151(4)=) = 2*11+ + 41.
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#41 by Jon E. Schoenfield at Mon Feb 19 11:24:45 EST 2024
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| NAME
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a(n) = 5*2^(n-1)-) - 2- - 3*n.
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| COMMENTS
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Create an array m(i,j) as follows: m(1,j) =) = j*(j-1)/2 in the top row, m(i,1) =() = (i-1)^2 in the left column, and m(i,j)=) = m(i,j-1) + m(i-1,j) recursively in the main body, j>= >= 1, i>= >= 1. The sum of the terms in an antidiagonal is one term in this sequence, a(n) = sumSum_{k=1..n} m(n-k+1,k).
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| FORMULA
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a(n) = A095151(n-1) + 2*A000295(n-1) .).
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proposed
editing
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#40 by Michel Marcus at Mon Feb 19 11:07:32 EST 2024
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#39 by Michel Marcus at Mon Feb 19 11:07:29 EST 2024
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| LINKS
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<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
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| FORMULA
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G.f. -.: -x^2*(2+x) / (2*x-1)*(x-1)^2 ). - R. J. Mathar, Jun 29 2012
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| EXAMPLE
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For n=5, m(5,1)=16, m(4,2)=15, m(3,3)=11, m(2,4)=11, m(1,5)=10 gives the sum 63=2*A000295(4)+A095151(4)=2*11+41.
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| CROSSREFS
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Cf. A000295, A095151, A000217, A000290.
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approved
editing
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