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 A136159 A Chebyshev polynomial triangle of the first kind defined by T(n+1,x) = 3x*T(n,x) - T(n-1,x). 1
 1, 1, 3, -1, 9, -4, 27, -15, 1, 81, -54, 7, 243, -189, 36, -1, 729, -648, 162, -10, 2187, -2187, 675, -66, 1, 6561, -7290, 2673, -360, 13, 19683, -24057, 10206, -1755, 105, -1, 59049, -78732, 37908, -7938, 675, -16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums (unsigned) give A003688, (starting 1, 1, 4, 13, 43, 142, 469, ...). LINKS Table of n, a(n) for n=0..41. FORMULA T(0,x) = 1, T(1,x) = x, T(n+1,x) = 3x*T(n,x) - T(n-1,x). G.f: (l - tx)/(1 - 3tx + t^2). Given triangle A136158, shift down columns to allow for (1, 1, 2, 2, 3, 3, ...) terms in each row. EXAMPLE First few rows of the polynomials are: 1; x; 3x^2 - 1; 9x^3 - 4x; 27x^4 - 15x^2 + 1; 81x^5 - 54x^3 + 7x; 243x^6 - 189x^4 + 36x^2 - 1; 729x^7 - 648x^5 + 162x^3 - 10x; ... PROG (PARI) P(n) = if (n==0, 1, if (n==1, x, 3*x*P(n-1) - P(n-2))); row(n) = select(x->x!=0, Vec(P(n))); \\ Michel Marcus, Apr 15 2018 CROSSREFS Cf. A136158, A003688. Cf. A000244, A006234, A080419, A080420, A080421, A080422, A080423. [Philippe Deléham, Sep 12 2009] Sequence in context: A127550 A021317 A091579 * A005533 A331257 A112626 Adjacent sequences: A136156 A136157 A136158 * A136160 A136161 A136162 KEYWORD tabf,sign AUTHOR Gary W. Adamson, Dec 16 2007 EXTENSIONS Corrected and extended by Philippe Deléham, Sep 12 2009 Keyword tabf set by Michel Marcus, Apr 15 2018 STATUS approved

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Last modified December 3 01:44 EST 2023. Contains 367529 sequences. (Running on oeis4.)