OFFSET
0,3
COMMENTS
Conjecture: sequence is its own inverse. - R. J. Mathar, May 08 2019
REFERENCES
J. H. Conway, Postings to Math Fun Mailing List, Nov 25 1996 and Dec 02 1996.
LINKS
J. H. Conway, Allan Wechsler, Marc LeBrun, Dan Hoey, N. J. A. Sloane, On Kimberling Sums and Para-Fibonacci Sequences, Correspondence and Postings to Math-Fun Mailing List, Nov 1996 to Jan 1997
EXAMPLE
Take n=5: reading row 5 of A035513 backwards gives ... 23, 14, 9, 5, 4, 1, 3, -2, 5, -7, 12, -19, ..., which after adjusting the signs is row 7, so a(5) = 7.
MAPLE
A035513 := proc(r::integer, c::integer)
option remember;
if c = 1 then
A003622(r) ;
elif c > 1 then
A022342(1+procname(r, c-1)) ;
elif c < 1 then
procname(r, c+2)-procname(r, c+1) ;
end if;
end proc:
# search in A035513 for row with consecutive w1, w2
A035513inv := proc(w1::integer, w2::integer)
local r, c, W1, W2 ;
for r from 1 do
if A035513(r, 1) > w2 then
return -1 ;
end if;
for c from 1 do
W1 := A035513(r, c) ;
W2 := A035513(r, c+1) ;
if W1=w1 and W2=w2 then
return r-1 ;
elif W2 > w2 then
break;
end if;
end do:
end do:
end proc:
A269729 := proc(n)
option remember;
local c, W1, W2, r, n35513;
n35513 := n+1 ;
for c from 1 by -1 do
W1 := A035513(n35513, c) ;
W2 := A035513(n35513, c-1) ;
if W1 < 0 and abs(W2) > abs(W1) then
r := A035513inv(abs(W1), abs(W2)) ;
if r >= 0 then
return r;
end if;
end if;
end do:
end proc:
seq(A269729(n), n=0..120) ; # R. J. Mathar, May 08 2019
MATHEMATICA
W[n_, k_] := W[n, k] = Fibonacci[k+1] Floor[n*GoldenRatio] + (n-1)* Fibonacci[k];
Winv[w1_, w2_] := Winv[w1, w2] = Module[{r, c, W1, W2}, For[r = 1, True, r++, If[W[r, 1] > w2, Return[-1]]; For[c = 1, True, c++, W1 = W[r, c]; W2 = W[r, c+1]; If[W1 == w1 && W2 == w2, Return[r-1], If[W2 > w2, Break[]]]]]];
a[n_] := a[n] = Module[{c, W1, W2, r, nw}, nw = n+1; For[c = 1, True, c--, W1 = W[nw, c]; W2 = W[nw, c-1]; If[W1 < 0 && Abs[W2] > Abs[W1], r = Winv[Abs[W1], Abs[W2]]; If[r >= 0, Return[r]]]]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 120}] (* Jean-François Alcover, Aug 09 2023, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 08 2016
EXTENSIONS
Terms from a(18) on by R. J. Mathar, May 08 2019
STATUS
approved