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 A116521 Binomial transform of tetranacci sequence A000078. 1
 0, 0, 0, 1, 5, 17, 51, 148, 429, 1250, 3655, 10701, 31336, 91752, 268623, 786414, 2302262, 6739984, 19731685, 57765711, 169112717, 495088023, 1449400960, 4243211207, 12422263776, 36366946961, 106466490879, 311687250156 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS See also A115390, the binomial transform of tribonacci sequence A000073. Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0) = a(1) = a(2) = 0, a(3) = 1. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-8,6,-1). FORMULA a(n) = Sum_{k=0..n} C(n,k) * A000078(k). G.f.: x^3/(1-5*x+8*x^2-6*x^3+x^4). - Emeric Deutsch, Apr 09 2006 a(n) = 5*a(n-1) - 8*a(n-2) + 6*a(n-3) - a(n-4). - G. C. Greubel, Nov 03 2016 EXAMPLE Table shows the tetranacci numbers multiplied into rows of Pascal's triangle. 1*0 = 0. 1*0 + 1*0 = 0. 1*0 + 2*0 + 1*0 = 0. 1*0 + 3*0 + 3*0 + 1* 1 = 1. 1*0 + 4*0 + 6*0 + 4*1 + 1*1 = 5. 1*0 + 5*0 + 10*0 + 10*1 + 5*1 + 1*2 = 17. MAPLE t[0]:=0: t[1]:=0: t[2]:=0: t[3]:=1: for n from 4 to 35 do t[n]:=t[n-1]+t[n-2]+t[n-3]+t[n-4] od: seq(add(binomial(n, k)*t[k], k=0..n), n=0..30); # end of first Maple program G:=x^3/(1-5*x+8*x^2-6*x^3+x^4): Gser:=series(G, x=0, 33): seq(coeff(Gser, x, n), n=0..30); # Emeric Deutsch, Apr 09 2006 MATHEMATICA LinearRecurrence[{5, -8, 6, -1}, {0, 0, 0, 1}, 25] (* G. C. Greubel, Nov 03 2016 *) PROG (PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 6, -8, 5]^n*[0; 0; 0; 1])[1, 1] \\ Charles R Greathouse IV, Jun 28 2017 CROSSREFS Cf. A000073, A000078, A115390. Sequence in context: A039783 A374185 A103685 * A290900 A137500 A146814 Adjacent sequences: A116518 A116519 A116520 * A116522 A116523 A116524 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Mar 10 2006 EXTENSIONS Definition corrected by Franklin T. Adams-Watters, Mar 13 2006 More terms from Emeric Deutsch, Apr 09 2006 STATUS approved

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Last modified September 10 06:17 EDT 2024. Contains 375773 sequences. (Running on oeis4.)