This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A206603 Maximal apex value of an addition triangle whose base is a permutation of {k-n/2, k=0..n}. 2
 0, 0, 1, 4, 13, 36, 94, 232, 557, 1300, 2986, 6744, 15074, 33320, 73116, 159184, 344701, 742068, 1590898, 3395320, 7222550, 15308920, 32362276, 68213424, 143463378, 300999816, 630353764, 1317415792, 2748991012, 5726300880, 11911913912, 24742452128, 51331847709 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The base row of the addition triangle contains a permutation of the n+1 integers or half-integers {k-n/2, k=0..n}.  Each number in a higher row is the sum of the two numbers directly below it.  Rows above the base row contain only integers.  The base row consists of integers iff n is even. Because of symmetry, a(n) is also the absolute value of the minimal apex value of an addition triangle whose base is a permutation of {k-n/2, k=0..n}. a(n) is odd iff n = 2^m and m > 0. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{k=0..n} C(n,floor(k/2)) * (k-n/2). G.f.: (1-sqrt(1-4*x^2)) / (2*(2*x-1)^2). a(n) = A189390(n)-A001787(n) = A001787(n)-A189391(n) = (A189390(n)-A189391(n))/2 = (A206604(n)-1)/2. EXAMPLE a(3) =  4:   max:      4            min:    -4                     1    3               -1   -3                 -1    2    1           1   -2   -1             -3/2  1/2  3/2 -1/2    3/2 -1/2 -3/2  1/2 a(4) = 13:   max:     13            min:   -13                      5  8                 -5 -8                    0  5  3               0 -5 -3                 -2  2  3  0            2 -2 -3  0               -2  0  2  1 -1         2  0 -2 -1  1 MAPLE a:= n-> add (binomial(n, floor(k/2))*(k-n/2), k=0..n): seq (a(n), n=0..40); # second Maple program: a:= proc(n) option remember; `if`(n<3, n*(n-1)/2,       ((2*n^2-6)*a(n-1) +4*(n-1)*(n-4)*a(n-2)        -8*(n-1)*(n-2)*a(n-3)) / (n*(n-2)))     end: seq(a(n), n=0..40); # Alois P. Heinz, Apr 25 2013 CROSSREFS Cf. A001787, A189390, A189391, A206604. Sequence in context: A036643 A000299 A102301 * A271176 A031506 A251701 Adjacent sequences:  A206600 A206601 A206602 * A206604 A206605 A206606 KEYWORD nonn AUTHOR Alois P. Heinz, Feb 10 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 01:03 EST 2019. Contains 329977 sequences. (Running on oeis4.)