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 A087401 Triangle of n*r-binomial(r+1,2). 5
 0, 0, 0, 0, 1, 1, 0, 2, 3, 3, 0, 3, 5, 6, 6, 0, 4, 7, 9, 10, 10, 0, 5, 9, 12, 14, 15, 15, 0, 6, 11, 15, 18, 20, 21, 21, 0, 7, 13, 18, 22, 25, 27, 28, 28, 0, 8, 15, 21, 26, 30, 33, 35, 36, 36, 0, 9, 17, 24, 30, 35, 39, 42, 44, 45, 45, 0, 10, 19, 27, 34, 40, 45, 49, 52, 54, 55, 55, 0, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS There is a curious connection with the character tables of cyclic groups of prime power order. Let G be a cyclic group of order p^n where p is prime and n is nonnegative. Construct an (n+1)x(n+1) matrix A whose rows and columns are indexed by the set 0,1,...,n as follows. The ij entry is obtained by taking any element of order p^(n-j) in G and summing its character values over all characters of order p^i in the dual group of G. Remarkably, all coefficients of the characteristic polynomial of A are powers of p (with alternating signs) and these powers can be read off from the appropriate row of our triangle. For example if n=2 then the characteristic polynomial is X^3 - p^2*X^2 + p^3*X - p^3. LINKS Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened FORMULA T(0,0)=0 and for n>0: T(n,k)=T(n-1,k)+k for k

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Last modified December 5 01:43 EST 2022. Contains 358572 sequences. (Running on oeis4.)