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

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A341260 Wythoff ceiling array; see Comments. 3
 2, 4, 5, 6, 9, 7, 10, 14, 12, 10, 16, 23, 19, 17, 13, 26, 37, 31, 27, 22, 15, 42, 60, 50, 44, 35, 25, 18, 68, 97, 81, 71, 57, 40, 30, 20, 110, 157, 131, 115, 92, 65, 48, 33, 23, 178, 254, 212, 186, 149, 105, 78, 53, 38, 26, 288, 411, 343, 301, 241, 170, 126 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Wythoff array, A035513, is given by W(n,k) = F(k+1)*floor(n*r) + (n - 1)*F(k), where F = A000045, the Fibonacci numbers. The Wythoff ceiling array, W*, is defined by W*(n,k) = F(k+1)*ceiling(n*r) + (n - 1)*F(k). This is a subarray of W; viz., row n of W* is row A001950(n) + 1 of the extended Wythoff array shown at A035513. Column 1: A001950 (upper Wythoff sequence). Some numbers, as in A341261, occur twice in W*, but none occurs more than twice. The set of numbers not in W* is given by A341262. LINKS FORMULA W*(n,k) = F(k+1)*ceiling(n*r) + (n - 1)*F(k), where F = A000045, the Fibonacci numbers. EXAMPLE Corner: 2 4 6 10 16 26 42 68 110 178 288 5 9 14 23 37 60 97 157 254 411 665 7 12 19 31 50 81 131 212 343 555 898 10 17 27 44 71 115 186 301 487 788 1275 13 22 35 57 92 149 241 390 631 1021 1652 15 25 40 65 105 170 275 445 720 1165 1885 18 30 48 78 126 204 330 534 864 1398 2262 20 33 53 86 139 225 364 589 953 1542 2495 23 38 61 99 160 259 419 678 1097 1775 2872 26 43 69 112 181 293 474 767 1241 2008 3249 MATHEMATICA W[n_, k_] := Fibonacci[k + 1] Ceiling[n*GoldenRatio] + (n - 1) Fibonacci[k]; Grid[Table[W[n, k], {n, 1, 20}, {k, 1, 18}]] (* A341260, as an array *) Table[W[n - k + 1, k], {n, 12}, {k, n, 1, -1}]; Flatten[w] (* A341260, as a sequence *) CROSSREFS Cf. A000045, A001950, A035513, A341261, A341262. Sequence in context: A244008 A104704 A169884 * A072726 A343585 A153242 Adjacent sequences: A341257 A341258 A341259 * A341261 A341262 A341263 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Feb 09 2021 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 November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)