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Search: id:A076822
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| A076822 |
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Number of partitions of the n-th triangular number involving only the numbers 1..n and with exactly n terms. |
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+0
2
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| 1, 1, 2, 5, 12, 32, 94, 289, 910, 2934, 9686, 32540, 110780, 381676, 1328980, 4669367, 16535154, 58965214, 211591218, 763535450, 2769176514, 10089240974, 36912710568, 135565151486, 499619269774, 1847267563742, 6850369296298
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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Max Alekseyev, Table of n, a(n) for n = 1..100
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FORMULA
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A067059(n,n+1). T[n*(n-1)/2, n-1, n] with T[ ] defined as in A047993. - Martin Fuller (martin_n_fuller(AT)btinternet.com), Jun 27 2006
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EXAMPLE
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a(4)=5 as T(4)=10= 1+1+4+4 =1+2+3+4 = 1+3+3+3 = 2+2+2+4 = 2+2+3+3.
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; f[n_] := Block[{p = Partitions[n(n + 1)/2, n]}, Length[ Select[p, Length[ # ] == n &]]]; Table[ f[n], {n, 1, 13}]
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PROGRAM
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[JavaScript] ccc=new Array(); cccc=0; for (n=1; n<11; n++) { str='cc=0; for (i1=1; i1<'+(n+1)+'; i1++)'; str2='i1'; str3='i1'; tn=1; for (i=2; i<=n; i++) { str+='for (i'+i+'=i'+(i-1)+'; i'+i+'<'+(n+1)+'; i'+i+'++)'; str2+='+i'+i; str3+=', ", ", i'+i; tn+=i; } str+='if ('+str2+'=='+tn+') document.write(++cc, ":", '+str3+', "<br>")'; eval(str); ccc[cccc++ ]=cc; document.write('****<br>'); } document.write(ccc);
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CROSSREFS
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Cf. A067059, A047993, A039744.
Sequence in context: A000840 A039809 A002838 this_sequence A014326 A115523 A010843
Adjacent sequences: A076819 A076820 A076821 this_sequence A076823 A076824 A076825
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Nov 19 2002
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EXTENSIONS
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Edited and extended to 12 terms by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 23 2002
Further terms from Max Alekseyev, May 24 2007
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