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A254967 Triangle of iterated absolute differences of lucky numbers read by antidiagonals upwards. 6
1, 2, 3, 2, 4, 7, 0, 2, 2, 9, 0, 0, 2, 4, 13, 0, 0, 0, 2, 2, 15, 2, 2, 2, 2, 4, 6, 21, 2, 0, 2, 0, 2, 2, 4, 25, 2, 0, 0, 2, 2, 0, 2, 6, 31, 0, 2, 2, 2, 0, 2, 2, 4, 2, 33, 0, 0, 2, 0, 2, 2, 0, 2, 2, 4, 37, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 6, 43, 2, 2, 2, 2, 0, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence is related to the lucky numbers (cf. A000959) in the same way as A036262 is related to the prime numbers;

T(n,0) = A054978(n);

T(2*n,n) = A254969(n);

T(n,n-1) = A031883(n), n > 0;

T(n,n) = A000959(n+1);

for n > 0: T(n,k) = abs(T(n,k+1) - T(n-1,k), k = 0 .. n-1.

LINKS

Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Eric Weisstein's World of Mathematics, Lucky number.

Wikipedia, Lucky number

EXAMPLE

.   0:                      1

.   1:                     2 3

.   2:                    2 4 7

.   3:                   0 2 2 9

.   4:                  0 0 2 4 13

.   5:                 0 0 0 2 2 15

.   6:                2 2 2 2 4 6 21

.   7:               2 0 2 0 2 2 4 25

.   8:              2 0 0 2 2 0 2 6 31

.   9:             0 2 2 2 0 2 2 4 2 33

.  10:            0 0 2 0 2 2 0 2 2 4 37

.  11:           0 0 0 2 2 0 2 2 0 2 6 43

.  12:          2 2 2 2 0 2 2 0 2 2 0 6 49

.  13:         0 2 0 2 0 0 2 0 0 2 4 4 2 51 .

MATHEMATICA

nmax = 13; (* max index for triangle rows *)

imax = 25; (* max index for initial lucky array L *)

L = Table[2i + 1, {i, 0, imax}];

For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]];

T[n_, n_] := If[n+1 <= Length[L], L[[n+1]], Print["imax should be increased"]; 0];

T[n_, k_] := T[n, k] = Abs[T[n, k+1] - T[n-1, k]];

Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Sep 22 2021 *)

PROG

(Haskell)

a254967 n k = a254967_tabl !! n !! k

a254967_row n = a254967_tabl !! n

a254967_tabl = diags [] $

   iterate (\lds -> map abs $ zipWith (-) (tail lds) lds) a000959_list

   where diags uss (vs:vss) = (map head wss) : diags (map tail wss) vss

                              where wss = vs : uss

CROSSREFS

Cf. A054978 (left edge), A254969 (central terms), A000959 (right edge), A031883, A036262.

Sequence in context: A192298 A341098 A353330 * A229012 A207606 A303845

Adjacent sequences:  A254964 A254965 A254966 * A254968 A254969 A254970

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Feb 11 2015

STATUS

approved

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Last modified August 10 03:38 EDT 2022. Contains 356029 sequences. (Running on oeis4.)