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A047662 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. 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 (list; table; graph; refs; listen; history; text; internal format)
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), 250-260.

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(n-1, k-1)+A047662(n, k-1)+A047662(n-1, k)+1; fi; end;

MATHEMATICA

a[n_, 1] := n; a[1, k_] := k; a[n_, k_] := a[n, k] = a[n-1, k-1] + a[n-1, k] + a[n, k-1] + 1; Table[ a[n-k+1, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Jean-Fran├žois 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 * A183474 A294034 A210220

Adjacent sequences:  A047659 A047660 A047661 * A047663 A047664 A047665

KEYWORD

nonn,tabl,nice,easy

AUTHOR

Don Knuth, N. J. A. Sloane

STATUS

approved

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Last modified August 20 18:56 EDT 2019. Contains 326154 sequences. (Running on oeis4.)