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A085697 a(n) = T(n+2)^2, where T(n) = tribonacci numbers (A000073). 16
0, 0, 1, 1, 4, 16, 49, 169, 576, 1936, 6561, 22201, 75076, 254016, 859329, 2907025, 9834496, 33269824, 112550881, 380757169, 1288092100, 4357584144, 14741602225, 49870482489, 168710633536, 570743986576, 1930813074369, 6531893843049 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

R. Schumacher, Explicit formulas for sums involving the squares of the first n Tribonacci numbers, Fib. Q., 58:3 (2020), 194-207.

LINKS

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (2,3,6,-1,0,-1)

FORMULA

G.f.: x^2*( 1-x-x^2-x^3 ) / ( (x^3+x^2+3*x-1)*(x^3-x^2-x-1) ).

a(n+6) = 2 a(n+5) + 3 a(n+4) + 6 a(n+3) - a(n+2) - a(n).

a(n) = (-A057597(n)+3*A057597(n+1)+6*A057597(n+2)+5*A113300(n+1)-A099463(n))/11. [From R. J. Mathar, Aug 19 2008]

MATHEMATICA

LinearRecurrence[{2, 3, 6, -1, 0, -1}, {0, 0, 1, 1, 4, 16}, 30] (* Harvey P. Dale, Oct 26 2020 *)

PROG

(Maxima) t[0]:1$

t[1]:1$

t[2]:2$

t[n]:=t[n-1]+t[n-2]+t[n-3]$

  makelist(t[n]^2, n, 0, 12); /* Emanuele Munarini, Mar 01 2011 */

CROSSREFS

Cf. A000073.

Sequence in context: A188501 A283692 A173712 * A262268 A231156 A271483

Adjacent sequences:  A085694 A085695 A085696 * A085698 A085699 A085700

KEYWORD

easy,nonn

AUTHOR

Emanuele Munarini, Jul 18 2003

EXTENSIONS

Offset corrected to match A000073. - N. J. A. Sloane, Sep 12 2020

STATUS

approved

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Last modified May 14 19:53 EDT 2021. Contains 343903 sequences. (Running on oeis4.)