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Search: id:A145515
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| A145515 |
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Square array A(n,k), n>=0, k>=0, read by antidiagonals: A(n,k) is the number of partitions of k^n into powers of k. |
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7
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| 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 4, 1, 1, 1, 2, 5, 10, 1, 1, 1, 2, 6, 23, 36, 1, 1, 1, 2, 7, 46, 239, 202, 1, 1, 1, 2, 8, 82, 1086, 5828, 1828, 1, 1, 1, 2, 9, 134, 3707, 79326, 342383, 27338, 1, 1, 1, 2, 10, 205, 10340, 642457, 18583582, 50110484, 692004, 1, 1, 1, 2, 11
(list; table; graph; listen)
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OFFSET
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0,8
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..860
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FORMULA
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See program.
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EXAMPLE
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A(2,3) = 5, because there are 5 partitions of 3^2=9 into powers of 3: 1+1+1+1+1+1+1+1+1, 1+1+1+1+1+1+3, 1+1+1+3+3, 3+3+3, 9.
Square array A(n,k) begins:
1 1 1 1 1 1 ...
1 1 2 2 2 2 ...
1 1 4 5 6 7 ...
1 1 10 23 46 82 ...
1 1 36 239 1086 3707 ...
1 1 202 5828 79326 642457
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MAPLE
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g:= proc(b, n, k) option remember; local t; if b<0 then 0 elif b=0 or n=0 or k<=1 then 1 elif b>=n then add (g(b-t, n, k) *binomial (n+1, t) *(-1)^(t+1), t=1..n+1); else g(b-1, n, k) +g(b*k, n-1, k) fi end: A:= (n, k)-> g(1, n, k): seq (seq (A(n, d-n), n=0..d), d=0..13);
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CROSSREFS
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Columns 0+1, 2-10 give: A000012, A002577, A078125, A078537, A111822, A111827, A111832, A111837, A145512, A145513. Diagonal gives: A145514. Cf. A007318.
Sequence in context: A129176 A134132 A030424 this_sequence A026519 A025177 A026148
Adjacent sequences: A145512 A145513 A145514 this_sequence A145516 A145517 A145518
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 11 2008
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