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A035311 First column of the Zorach additive triangle A035312. 9
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Dec 02 2011 *)

PROG

See link for Haskell program.

CROSSREFS

Cf. A035312, A035313, A189713, A035358.

Sequence in context: A011178 A136790 A073158 * A182310 A244591 A299324

Adjacent sequences:  A035308 A035309 A035310 * A035312 A035313 A035314

KEYWORD

nonn,easy,nice

AUTHOR

Alex Zorach

EXTENSIONS

More terms from Christian G. Bower

STATUS

approved

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Last modified January 19 09:12 EST 2021. Contains 340267 sequences. (Running on oeis4.)