A035311 First column of the Zorach additive triangle A035312.

1, 2, 4, 7, 5, 8, 10, 14, 15, 19, 16, 20, 21, 22, 27, 30, 28, 33, 32, 38, 37, 39, 44, 45, 51, 46, 47, 54, 55, 52, 59, 62, 60, 64, 50, 67, 72, 78, 74, 68, 81, 82, 80, 85, 79, 87, 86, 91, 90, 94, 102, 98, 103, 99, 105, 100, 108, 112, 110, 113, 127, 128, 125, 133, 118, 123

Offset

0,2

Comments

One can see that (least unused number in rows 1 through n of A035312) ~ A035311(n) ~ 2n. (Asymptotic equality, and the first quantity does not exceed either of the two others.) - M. F. Hasler, May 09 2013

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

A. C. Zorach, Additive triangle

Haskell programs for sequences in connection with Zorach additive triangle

Mathematica

(* Assuming n <= t(n, 1) <= 3n *) uniqueQ[t1_, n_] := (t[n, 1] = t1; Do[t[n, k] = t[n, k-1] + t[n-1, k-1], {k, 2, n}]; n*(n+1)/2 == Length[ Union[ Flatten[ Table[ t[m, k], {m, 1, n}, {k, 1, m}]]]]); t[n_ , 1] := t[n, 1] = Select[ Complement[ Range[n, 3 n], Flatten[ Table[t[m, k], {m, 1, n - 1}, {k, 1, m}]]], uniqueQ[#, n] & , 1][[1]]; Table[t[n, 1], {n, 1, 66}](* Jean-François Alcover, Dec 02 2011 *)

Prog

(Haskell) -- See link for Haskell program.

Crossrefs

Cf. A035312, A035313, A189713, A035358.

Sequence in context: A011178 A136790 A073158 * A182310 A244591 A377351

Adjacent sequences: A035308 A035309 A035310 * A035312 A035313 A035314

Keyword

nonn,easy,nice

Author

Alex Zorach

Extensions

More terms from Christian G. Bower

Status

approved