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Search: id:A064861
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| A064861 |
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Triangle of Sulanke numbers: a(m,n)=a(m,n-1)+a(m-1,n) for m+n even and a(m,n)=a(m,n-1)+2a(m-1,n) for m+n odd. |
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+0
8
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| 1, 1, 2, 1, 3, 2, 1, 5, 8, 4, 1, 6, 13, 12, 4, 1, 8, 25, 38, 28, 8, 1, 9, 33, 63, 66, 36, 8, 1, 11, 51, 129, 192, 168, 80, 16, 1, 12, 62, 180, 321, 360, 248, 96, 16, 1, 14, 86, 304, 681, 1002, 968, 592, 208, 32, 1, 15, 100, 390, 985, 1683, 1970, 1560, 800, 240, 32, 1, 17
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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When A064861 is regarded as a triangle read by rows, this is [1,0,-1,0,0,0,0,0,0,...] DELTA [2,-1,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 14 2008]
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REFERENCES
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R. A. Sulanke, Problem 10894, Amer. Math. Monthly 108, (2001), p. 770.
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FORMULA
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G.f.: sum_{m=0}^infinity sum_{n=0}^infinity a_{m, n}t^m s^n=A(t, s)=(1+2t+s)/(1-2t^2-s^2-3st)
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EXAMPLE
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Table begins:
1 1 1 1 1 1 1 1 ...
2 3 5 6 8 9 11 ...
2 8 13 25 33 51 ...
4 12 38 63 129 ...
4 28 66 192 ...
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MAPLE
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A064861 := proc(n, k) option remember; if n = 1 then 1; elif k = 0 then 0; else A064861(n, k-1)+(3/2-1/2*(-1)^(n+k))*A064861(n-1, k); fi; end; seq(seq(A064861(i, j-i), i=1..j-1), j=1..19);
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PROGRAM
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(PARI) a(n, m)=if(n<0|m<0, 0, polcoeff(polcoeff((1+2*x+y*x)/(1-2*x^2-y^2*x^2-3*y*x^2)+O(x^(n+m+1)), n+m), m))
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CROSSREFS
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Cf. central Delannoy numbers a(n, n)=A001850(n), Delannoy numbers (same main diagonal): a(n, n)=A008288(n, n), a(n-1, n)=A002003(n), a(n, n+1)=A002002(n), a(n, 1)=A058582(n), apparently a(n, n+2)=A050151(n).
Sequence in context: A061260 A152097 A119442 this_sequence A070979 A054098 A132089
Adjacent sequences: A064858 A064859 A064860 this_sequence A064862 A064863 A064864
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KEYWORD
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nonn,tabl,nice
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AUTHOR
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Barbara Haas Margolius (b.margolius(AT)csuohio.edu), Oct 10, 2001
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