The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. EXAMPLE The array begins: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ... 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, ... 3, 12, 31, 64, 115, 188, 287, 416, 579, 780, 1023, 1312, ... 4, 20, 64, 160, 340, 644, 1120, 1824, 2820, 4180, 5984, 8320, ... 5, 30, 115, 340, 841, 1826, 3591, 6536, 11181, 18182, 28347, 42652, ... 6, 42, 188, 644, 1826, 4494, 9912, 20040, 37758, 67122, 113652, 184652, ... 7, 56, 287, 1120, 3591, 9912, 24319, 54272, 112071, 216952, 397727, 696032, ... 8, 72, 416, 1824, 6536, 20040, 54272, 132864, 299208, 628232, 1242912, 2336672, ... ... The first few antidiagonals are: 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, ... 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-François Alcover, Aug 13 2013 *) CROSSREFS Rows give A037237, 4*A006007, A047661, A047663, A047664, main diagonal is A047665 (see also A001850). See also A008288, A048776. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 28 21:07 EDT 2023. Contains 363028 sequences. (Running on oeis4.)