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Search: id:A134574
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| A134574 |
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Array, a(n,k) = total size of all n-length words on a k-letter alphabet, read by anti-diagonals. |
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+0
3
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| 1, 2, 2, 3, 8, 3, 4, 24, 18, 4, 5, 64, 81, 32, 5, 6, 160, 324, 192, 50, 6, 7, 384, 1215, 1024, 375, 72, 7, 8, 896, 4374, 5120, 2500, 648, 98, 8, 9, 2048, 15309, 24576, 15625, 5184, 1029, 128, 9, 10, 4608, 52488, 114688, 93750, 38880, 9604, 1536, 162, 10
(list; table; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n,k) = n*k^n. O.g.f. (by columns) is (kx)/(-1+kx)^2. E.g.f. (by columns) is kx*(e^kx).
a(n,k) = Sum[k^n,{j,1,n}] = n*Sum[C(n,m)*(k-1)^m,{m,0,n}]. - Ross La Haye (rlahaye(AT)new.rr.com), Jan 26 2008
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EXAMPLE
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a(2,2) = 8 because there are 2^2 = 4 2-length words on a 2 letter alphabet, each of size 2, and 2*4 = 8.
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CROSSREFS
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Cf. a(n, 1) = a(1, k) = A000027(n); a(n, 2) = A036289(n); a(n, 3) = A036290(n); a(n, 4) = A018215(n); a(n, 5) = A036291(n); a(n, 6) = A036292(n); a(n, 7) = A036293(n); a(n, 8) = A036294(n); a(2, k) = A001105(k); a(3, k) = A117642(k); a(n, n) = A007778(n); a(n, n+1) = A066274(n+1): sum[a(i-1, n-i+1), {i, 1, n}] = A062807(n).
Adjacent sequences: A134571 A134572 A134573 this_sequence A134575 A134576 A134577
Sequence in context: A110985 A141611 A135835 this_sequence A141617 A100551 A070267
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KEYWORD
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nonn,tabl
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AUTHOR
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Ross La Haye (rlahaye(AT)new.rr.com), Jan 22 2008
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