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Search: id:A048483
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| A048483 |
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Array read by antidiagonals: T(k,n) = (k+1)2^n - k. |
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+0
10
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| 1, 2, 1, 4, 3, 1, 8, 7, 4, 1, 16, 15, 10, 5, 1, 32, 31, 22, 13, 6, 1, 64, 63, 46, 29, 16, 7, 1, 128, 127, 94, 61, 36, 19, 8, 1, 256, 255, 190, 125, 76, 43, 22, 9, 1, 512, 511, 382, 253, 156, 91, 50, 25, 10, 1, 1024, 1023, 766, 509, 316, 187
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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n-th difference of (T(k,n),T(k,n-1),...,T(k,0)) is k+1, for n=1,2,3,...; k=0,1,2,...
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FORMULA
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G.f.: (1-x+kx)/[(1-x)(1-2x)]. E.g.f.: (k+1)*exp(2x) - k*exp(x).
Recurrences: T(k, n) = 2T(k, n-1)+k = T(k-1, n)+2^n-1, T(k, 0) = 1.
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EXAMPLE
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1 2 4 8 16 32 ...
1 3 7 15 31 63 ...
1 4 10 22 46 94 ...
1 5 13 29 61 125 ...
1 6 16 36 76 156 ...
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CROSSREFS
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Rows are A000079 (k=0), A000225 (k=1), A033484 (k=2), A036563 (k=3), A048487 (k=4), A048488 (k=5), A048489 (k=6), A048490 (k=7), A048491 (k=8).
Main diagonal is A048493. Cf. A048494.
Sequence in context: A115450 A109435 A134392 this_sequence A055248 A103316 A140069
Adjacent sequences: A048480 A048481 A048482 this_sequence A048484 A048485 A048486
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Edited by Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 05 2004
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