The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A253026 T(n,k) = Number of n X k nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 1 and every value within 1 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down. 3
 0, 1, 1, 2, 1, 2, 3, 5, 5, 3, 4, 9, 5, 9, 4, 5, 13, 21, 21, 13, 5, 6, 17, 37, 21, 37, 17, 6, 7, 21, 53, 85, 85, 53, 21, 7, 8, 25, 69, 149, 85, 149, 69, 25, 8, 9, 29, 85, 213, 341, 341, 213, 85, 29, 9, 10, 33, 101, 277, 597, 341, 597, 277, 101, 33, 10, 11, 37, 117, 341, 853, 1365 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS R. H. Hardin, Table of n, a(n) for n = 1..10018 Aaron Barnoff, Curtis Bright, and Jeffrey Shallit, Using finite automata to compute the base-b representation of the golden ratio and other quadratic irrationals, arXiv:2405.02727 [cs.FL], 2024. See p. 8. Robert Dougherty-Bliss, Experimental Methods in Number Theory and Combinatorics, Ph. D. Dissertation, Rutgers Univ. (2024). See p. 21. Robert Dougherty-Bliss and Manuel Kauers, Hardinian Arrays, arXiv:2309.00487 [math.CO], 2023, Hardinian Arrays, El. J. Combinat. 31 (2) (2024) #P2.9 FORMULA T(n,k) = (n-k)*4^(k-1) + (4^(k-1)-1)/3 for all n>=k>=1 (Thm. 2 in the paper of Dougerty-Bliss and Kauers cited above). - Manuel Kauers, Sep 06 2023 T(n,k) = T(k,n) for all n,k. EXAMPLE Table starts: .0..1...2...3....4....5.....6.....7.....8.....9.....10.....11.....12......13 .1..1...5...9...13...17....21....25....29....33.....37.....41.....45......49 .2..5...5..21...37...53....69....85...101...117....133....149....165.....181 .3..9..21..21...85..149...213...277...341...405....469....533....597.....661 .4.13..37..85...85..341...597...853..1109..1365...1621...1877...2133....2389 .5.17..53.149..341..341..1365..2389..3413..4437...5461...6485...7509....8533 .6.21..69.213..597.1365..1365..5461..9557.13653..17749..21845..25941...30037 .7.25..85.277..853.2389..5461..5461.21845.38229..54613..70997..87381..103765 .8.29.101.341.1109.3413..9557.21845.21845.87381.152917.218453.283989..349525 .9.33.117.405.1365.4437.13653.38229.87381.87381.349525.611669.873813.1135957 Some solutions for n=4 and k=4: ..0..1..2..2....0..1..1..2....0..0..1..2....0..1..2..2....0..1..1..2 ..1..1..2..2....0..1..1..2....0..0..1..2....1..1..2..2....0..1..2..2 ..2..2..2..2....1..1..1..2....1..1..1..2....1..2..2..2....1..1..2..2 ..2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2....2..2..2..2 CROSSREFS Column 1 is A000027(n-1). Column 2 is A004766(n-2). Diagonal is A002450(n-1). Sequence in context: A075758 A125596 A351962 * A341145 A204994 A277253 Adjacent sequences: A253023 A253024 A253025 * A253027 A253028 A253029 KEYWORD nonn,tabl,changed AUTHOR R. H. Hardin, Dec 26 2014 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 23 04:41 EDT 2024. Contains 372758 sequences. (Running on oeis4.)