The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A066411 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A066411

Form a triangle with the numbers [0..n] on the base, where each number is the sum of the two below; a(n) is the number of different possible values for the apex.
(history; published version)

#72 by N. J. A. Sloane at Wed Oct 20 00:31:37 EDT 2021

STATUS

proposed

approved

#71 by Michel Marcus at Tue Oct 19 23:46:16 EDT 2021

STATUS

editing

proposed

#70 by Michel Marcus at Tue Oct 19 23:46:12 EDT 2021

NAME

Form a triangle with the numbers [0..n] on the base, where each number is the sum of the two below; a(n) = is the number of different possible values for the apex.

COMMENTS

a(n) = is the number of different possible sums of c_k * (n choose k) where the c_k are a permutation of 0 through n. - Joshua Zucker, May 08 2006

#69 by Michel Marcus at Tue Oct 19 23:45:38 EDT 2021

KEYWORD

nonn,nice,more,nonn,changed

STATUS

proposed

editing

#68 by Chai Wah Wu at Tue Oct 19 23:36:03 EDT 2021

STATUS

editing

proposed

#67 by Chai Wah Wu at Tue Oct 19 23:35:35 EDT 2021

CROSSREFS

Cf. A062684, A062896, A099325, A189162, A189390, (maximum apex value), A189391 (minimum apex value).

STATUS

proposed

editing

#66 by Michel Marcus at Tue Oct 19 23:18:56 EDT 2021

STATUS

editing

proposed

#65 by Michel Marcus at Tue Oct 19 23:18:24 EDT 2021

PROG

(PARI) A066411(n)={my(u=0, o=A189391(n), v, b=vector(n++, i, binomial(n-1, i-1))~); sum(k=1, n!\2, !bittest(u, numtoperm(n, k)*b-o) & u+=1<<(numtoperm(n, k)*b-o))} \\ - __M. F. Hasler_, Jan 24 2012

STATUS

proposed

editing

#64 by Chai Wah Wu at Tue Oct 19 23:16:31 EDT 2021

STATUS

editing

proposed

#63 by Chai Wah Wu at Tue Oct 19 23:11:33 EDT 2021

PROG

def partitionpairs(xlist): # generator of all partitions of xlist into pairs and at most 1 singleton, returning the sums of the pairs

yield [sum(xlist)]

y = [xlist[i]+xlist[j]]

yield [xlist[i], xlist[j]]+d

yield y+d

return len(set((sum(sum(d[2*i:2*i+2])*b[i] for i in range(n//2+1)) for d in partitionpairs(list(range(n+1)))))) # Chai Wah Wu, Oct 19 2021

STATUS

proposed

editing