A326296 Triangle of numbers T(n,k) = 2*floor(k/2)*(n-k) + ceiling((k-1)^2/2), 1<=k<=n.
0, 0, 1, 0, 3, 2, 0, 5, 4, 5, 0, 7, 6, 9, 8, 0, 9, 8, 13, 12, 13, 0, 11, 10, 17, 16, 19, 18, 0, 13, 12, 21, 20, 25, 24, 25, 0, 15, 14, 25, 24, 31, 30, 33, 32, 0, 17, 16, 29, 28, 37, 36, 41, 40, 41, 0, 19, 18, 33, 32, 43, 42, 49, 48, 51, 50, 0, 21, 20, 37, 36, 49, 48, 57, 56, 61, 60, 61
Offset: 1
Examples
Triangle begins: 0; 0, 1; 0, 3, 2; 0, 5, 4, 5; 0, 7, 6, 9, 8; 0, 9, 8, 13, 12, 13; 0, 11, 10, 17, 16, 19, 18; 0, 13, 12, 21, 20, 25, 24, 25; 0, 15, 14, 25, 24, 31, 30, 33, 32; 0, 17, 16, 29, 28, 37, 36, 41, 40, 41; 0, 19, 18, 33, 32, 43, 42, 49, 48, 51, 50; 0, 21, 20, 37, 36, 49, 48, 57, 56, 61, 60, 61; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
Crossrefs
Programs
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PARI
T(n,k) = {2*floor(k/2)*(n-k) + ceil((k-1)^2/2)} \\ Andrew Howroyd, Sep 10 2019
Formula
T(n,k) = 2*floor(k/2)*(n-k) + ceiling((k-1)^2/2).
T(n,k) = 2*floor(k/2)*(n-k) + binomial(k,2) - ceiling(k/2) + 1.
Comments