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A047662
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Square array a(n,k) read by antidiagonals: a(n,1)=n, a(1,k)=k, a(n,k)=a(n-1,k-1)+a(n-1,k)+a(n,k-1)+1.
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7
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1, 2, 2, 3, 6, 3, 4, 12, 12, 4, 5, 20, 31, 20, 5, 6, 30, 64, 64, 30, 6, 7, 42, 115, 160, 115, 42, 7, 8, 56, 188, 340, 340, 188, 56, 8, 9, 72, 287, 644, 841, 644, 287, 72, 9, 10, 90, 416, 1120, 1826, 1826, 1120, 416, 90, 10, 11, 110, 579, 1824, 3591
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| M. L. Fredman, The complexity of maintaining an array and its partial sums, J. Assoc. Comp. Machin., 29 (1982), 250-260.
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FORMULA
| a(n, k) =(A008288(n, k)-1)/2. Sum of antidiagonals is A048776.
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MAPLE
| A047662 := proc(n, k) option remember; if n = 1 then k; elif k = 1 then n; else A047662(n-1, k-1)+A047662(n, k-1)+A047662(n-1, k)+1; fi; end;
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CROSSREFS
| Rows give A037237, 4*A006007, A047661, A047663, A047664, main diagonal is A047665 (see also A001850).
Sequence in context: A190098 A125102 A003506 * A183474 A075196 A196912
Adjacent sequences: A047659 A047660 A047661 * A047663 A047664 A047665
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KEYWORD
| nonn,tabl,nice,easy
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AUTHOR
| D. E. Knuth, N. J. A. Sloane (njas(AT)research.att.com).
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