

A047662


Square array a(n,k) read by antidiagonals: a(n,1)=n, a(1,k)=k, a(n,k)=a(n1,k1)+a(n1,k)+a(n,k1)+1.


8



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
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OFFSET

1,2


LINKS

Vincenzo Librandi, Rows n = 1..100, flattened
M. L. Fredman, The complexity of maintaining an array and its partial sums, J. Assoc. Comp. Machin., 29 (1982), 250260.
D. E. Knuth and N. J. A. Sloane, Correspondence, December 1999
Matthew Roughan, Surreal Birthdays and Their Arithmetic, arXiv:1810.10373 [math.HO], 2018.


FORMULA

a(n, k) =(A008288(n, k)1)/2. Sum of antidiagonals is A048776.


MAPLE

A047662 := proc(n, k) option remember; if n = 1 then k; elif k = 1 then n; else A047662(n1, k1)+A047662(n, k1)+A047662(n1, k)+1; fi; end;


MATHEMATICA

a[n_, 1] := n; a[1, k_] := k; a[n_, k_] := a[n, k] = a[n1, k1] + a[n1, k] + a[n, k1] + 1; Table[ a[nk+1, k], {n, 1, 11}, {k, 1, n}] // Flatten (* JeanFrançois Alcover, Aug 13 2013 *)


CROSSREFS

Rows give A037237, 4*A006007, A047661, A047663, A047664, main diagonal is A047665 (see also A001850).
Sequence in context: A296396 A125102 A003506 * A329655 A183474 A294034
Adjacent sequences: A047659 A047660 A047661 * A047663 A047664 A047665


KEYWORD

nonn,tabl,nice,easy


AUTHOR

Don Knuth, N. J. A. Sloane


STATUS

approved



