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A126256 Number of distinct terms in rows 0 through n of Pascal's triangle. 5
1, 1, 2, 3, 5, 7, 9, 12, 16, 20, 24, 29, 35, 41, 48, 53, 60, 68, 77, 86, 95, 103, 114, 125, 137, 149, 162, 175, 188, 202, 217, 232, 248, 264, 281, 297, 314, 332, 351, 370, 390, 410, 431, 452, 474, 495, 518, 541, 565, 589, 614, 639, 665, 691, 718, 744, 770, 798 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

An easy upper bound is 1 + floor(n^2/4) = A033638(n). First differences are in A126257.

LINKS

N. Hobson, Table of n, a(n) for n = 0..1000

N. Hobson, Home page (listed in lieu of email address)

Nick Hobson, Python program for this sequence

EXAMPLE

There are 9 distinct terms in rows 0 through 6 of Pascal's triangle (1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 20, 15, 6, 1); hence a(6)=9.

MAPLE

seq(nops(`union`(seq({seq(binomial(n, k), k=0..n)}, n=0..m))), m=0..57); # Emeric Deutsch, Aug 26 2007

PROG

(PARI) lim=57; z=listcreate(1+lim^2\4); for(n = 0, lim, for(r=1, n\2, s=Str(binomial(n, r)); f=setsearch(z, s, 1); if(f, listinsert(z, s, f))); print1(1+#z, ", "))

(Haskell)

-- import Data.List.Ordered (insertSet)

a126256 n = a126256_list !! n

a126256_list = f a007318_tabl [] where

   f (xs:xss) zs = g xs zs where

     g []     ys = length ys : f xss ys

     g (x:xs) ys = g xs (insertSet x ys)

-- Reinhard Zumkeller, May 26 2015, Nov 09 2011

CROSSREFS

Cf. A007318, A027424, A061786, A126254-A126257.

Cf. A199425.

Cf. A258318.

Sequence in context: A224854 A074752 A039825 * A062438 A102424 A237826

Adjacent sequences:  A126253 A126254 A126255 * A126257 A126258 A126259

KEYWORD

easy,nonn

AUTHOR

Nick Hobson, Dec 24 2006

STATUS

approved

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Last modified July 8 05:33 EDT 2020. Contains 335513 sequences. (Running on oeis4.)