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A082601
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Tribonacci array: to get next row, right-adjust previous 3 rows and add them, then append a final 0.
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2
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1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 0, 0, 1, 4, 6, 2, 0, 0, 1, 5, 10, 7, 1, 0, 0, 1, 6, 15, 16, 6, 0, 0, 0, 1, 7, 21, 30, 19, 3, 0, 0, 0, 1, 8, 28, 50, 45, 16, 1, 0, 0, 0, 1, 9, 36, 77, 90, 51, 10, 0, 0, 0, 0, 1, 10, 45, 112, 161, 126, 45, 4, 0, 0, 0, 0, 1, 11, 55, 156, 266, 266, 141, 30, 1, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Coefficients of tribonacci polynomials: t_0 = 1, t_1 = x, t_2 = x^2+x, t_n = x*(t_{n-1}+t_{n-2}+t_{n-3}).
Row sums are tribonacci numbers.
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REFERENCES
| Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001; Chapter 47: Tribonacci Polynomials: ("In 1973, V.E. Hoggatt, Jr. and M. Bicknell generalized Fibonacci polynomials to Tribonacci polynomials tx(x)"); Table 47.1, page 534: "Tribonacci Array".
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FORMULA
| G.f.: x/(1-x-x^2*y-x^3*y^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), May 30 2003
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EXAMPLE
| Triangle begins:
1,
1,0
1,1,0
1,2,1,0
1,3,3,0,0
1,4,6,2,0,0
1,5,10,7,1,0,0
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MAPLE
| G:=x*y/(1-x-x^2*y-x^3*y^2): Gs:=simplify(series(G, x=0, 18)): for n from 1 to 16 do P[n]:=sort(coeff(Gs, x^n)) od: seq(seq(coeff(P[i], y^j), j=1..i), i=1..16);
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CROSSREFS
| Closely related to A078802. A better version of A082870. Cf. A000073.
Sequence in context: A173438 A103493 A121480 * A077593 A119337 A110555
Adjacent sequences: A082598 A082599 A082600 * A082602 A082603 A082604
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 24 2003
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EXTENSIONS
| Edited by Anne Donovan and N. J. A. Sloane (njas(AT)research.att.com), May 27, 2003
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), May 06 2004
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