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 A103247 Triangle read by rows: T(n,k) is the coefficient of x^k (0<=k<=n) in the monic characteristic polynomial of the n X n matrix with 3's on the diagonal and 1's elsewhere (n>=1). Row 0 consists of the single term 1. 5
 1, -3, 1, 8, -6, 1, -20, 24, -9, 1, 48, -80, 48, -12, 1, -112, 240, -200, 80, -15, 1, 256, -672, 720, -400, 120, -18, 1, -576, 1792, -2352, 1680, -700, 168, -21, 1, 1280, -4608, 7168, -6272, 3360, -1120, 224, -24, 1, -2816, 11520, -20736, 21504, -14112, 6048, -1680, 288, -27, 1, 6144, -28160, 57600, -69120 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums of the unsigned triangle yield A006234. The unsigned triangle is the mirror image of A103407. LINKS FORMULA Appears to be the matrix product (I-S)*P^(-2), where I is the identity, P is Pascal's triangle A007318 and S is A132440, the infinitesimal generator of P. Cf. A055137 (= (I-S)*P) and A103283 (= (I-S)*P^(-1)). - Peter Bala, Nov 28 2011 EXAMPLE The monic characteristic polynomial of the matrix [3 1 1 / 1 3 1 / 1 1 3] is x^3 - 9x^2 + 24x - 20; so T(3,0)=-20, T(3,1)=24, T(3,2)=-9, T(3,3)=1. Triangle begins: 1; -3,1; 8,-6,1; -20,24,-9,1; 48,-80,48,-12,1; MAPLE with(linalg): a:=proc(i, j) if i=j then 3 else 1 fi end: 1; for n from 1 to 10 do seq(coeff(expand(x*charpoly(matrix(n, n, a), x)), x^k), k=1..n+1) od; # yields the sequence in triangular form CROSSREFS Cf. A006234, A103407. Sequence in context: A258018 A188939 A062196 * A030523 A207815 A125662 Adjacent sequences:  A103244 A103245 A103246 * A103248 A103249 A103250 KEYWORD sign,tabl AUTHOR Emeric Deutsch, Mar 19 2005 STATUS approved

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Last modified June 24 05:55 EDT 2021. Contains 345416 sequences. (Running on oeis4.)