A116521 Binomial transform of tetranacci sequence A000078.

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

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: A196333 A039783 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