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A061922
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Xcatalans - produced as a self-convolved sequence like Catalan numbers (A000108) but use carryless GF(2)[ X ] polynomial multiplication.
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6
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1, 1, 2, 5, 14, 42, 132, 421, 1382, 4478, 15580, 54114, 181676, 650484, 2289320, 8028901, 28045302, 103229014, 372640460, 1336511110, 4882492452, 17534836812, 63692926552, 234287550818, 868236370364, 3281589811404
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Shifts one place left when Xmult-convolved (XMULTCONV) with itself.
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MAPLE
| Xcatalans(30); Xcatalans := proc(upto_n) local a, i, k; a := [1]; for i from 1 to upto_n do a := [ op(a), add(Xmult(a[k], a[i-k+1]), k=1..i)]; od; RETURN(a); end;
XMULTCONV := proc(a, b) local c, i, k, n; n := min( nops(a), nops(b) ); c := []; for i from 0 to n-1 do c := [ op(c), add(Xmult(a[k+1], b[i-k+1]), k=0..i)]; od; RETURN(c); end;
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CROSSREFS
| For Xmult, see A048720 (Xmult table) or A048631 (Xfactorials). Other self-convolved sequences: A000108, A007460 - A007464, A025192.
Sequence in context: A054392 A006930 A036767 * A162746 A148329 A024175
Adjacent sequences: A061919 A061920 A061921 * A061923 A061924 A061925
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KEYWORD
| nonn,easy,eigen
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AUTHOR
| Antti Karttunen May 15 2001
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