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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

Table of n, a(n) for n=1..62.

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

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Last modified November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)