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Search: id:A135298
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| A135298 |
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a(n) = the total number of permutations (m(1),m(2),m(3)...m(j)) of (1,2,3,...,j) where n = 1*m(1) + 2*m(2) + 3*m(3) + ...+j*m(j), where j is over all positive integers. |
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1
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| 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 1, 3, 1, 4, 2, 2, 2, 4, 1, 3, 1, 0, 0, 0, 0, 1, 4, 3, 6, 7, 6, 4, 10, 6, 10, 6, 10, 6, 10, 4, 6, 7, 6, 3, 4, 1, 1, 5, 6, 9, 16, 12, 14, 24, 20, 21, 23, 28, 24, 34, 20, 32, 42, 29, 29, 42, 32, 20, 34, 24, 28, 23, 21, 20, 25, 20, 22, 30, 38
(list; graph; listen)
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OFFSET
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1,11
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COMMENT
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Does every integer greater than some positive integer N have at least one such representation?
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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21 has a(21)=3 such representations: 21 = 1*4 + 2*3 + 3*1 + 4*2 = 1*4 + 2*2 + 3*3 + 4*1 = 1*3 + 2*4 + 3*2 + 4*1.
Not all representations of an integer n need to necessarily have the same j. For example, 91 = 1*1 + 2*2 + 3*3 + 4*4 + 5*5 + 6*6 (j=6). And 91 also equals 1*7 + 2*4 + 3*5 + 4*3 + 5*6 + 6*2 + 7*1 (j=7).
1 = 1*1;
4 = 1*2+2*1;
5 = 1*1+2*2;
10 = 1*3+2*2+3*1;
11 = 1*2+2*3+3*1;
11 = 1*3+2*1+3*2;
13 = 1*1+2*3+3*2;
13 = 1*2+2*1+3*3;
14 = 1*1+2*2+3*3;
20 = 1*4+2*3+3*2+4*1;
21 = 1*3+2*4+3*2+4*1;
21 = 1*4+2*2+3*3+4*1;
21 = 1*4+2*3+3*1+4*2;
22 = 1*3+2*4+3*1+4*2;
23 = 1*2+2*4+3*3+4*1;
23 = 1*3+2*2+3*4+4*1;
23 = 1*4+2*1+3*3+4*2;
23 = 1*4+2*2+3*1+4*3;
24 = 1*2+2*3+3*4+4*1;
24 = 1*4+2*1+3*2+4*3;
25 = 1*2+2*4+3*1+4*3;
25 = 1*3+2*1+3*4+4*2;
26 = 1*1+2*4+3*3+4*2;
26 = 1*3+2*2+3*1+4*4;
27 = 1*1+2*3+3*4+4*2;
27 = 1*1+2*4+3*2+4*3;
27 = 1*2+2*3+3*1+4*4;
27 = 1*3+2*1+3*2+4*4;
28 = 1*2+2*1+3*4+4*3;
29 = 1*1+2*2+3*4+4*3;
29 = 1*1+2*3+3*2+4*4;
29 = 1*2+2*1+3*3+4*4;
30 = 1*1+2*2+3*3+4*4;
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MAPLE
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A135298rec := proc(j, n, notm) local a, m ; a := 0 ; if n = 0 then if max( seq(e, e=notm) ) >= j then RETURN(0) ; else RETURN(1) ; fi ; end: for m from 1 do if n-j*m < 0 then break ; elif not m in notm then a := a+A135298rec(j+1, n-j*m, [op(notm), m] ) ; fi ; od: RETURN(a) ; end: A135298 := proc(n) A135298rec(1, n, []) ; end: for n from 1 to 140 do printf("%d, ", A135298(n)) ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 30 2008
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CROSSREFS
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Sequence in context: A137668 A056615 A060989 this_sequence A006996 A112604 A072627
Adjacent sequences: A135295 A135296 A135297 this_sequence A135299 A135300 A135301
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet, Dec 04 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 30 2008
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