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A172511 a(n) = a(n-1) * (11*a(n-1) - a(n-2)) / (a(n-1) + 4*a(n-2)), with a(0) = a(1) = 1. 2
1, 1, 2, 7, 35, 210, 1365, 9165, 62322, 425867, 2915551, 19974626, 136884937, 938162617, 6430103330, 44072167855, 302074043195, 2070443441970, 14191023001437, 97266699113157, 666675822475026, 4569463931720051 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-33,33,-11,1).

FORMULA

a(n) = (4 + A049685(n-1) + 5 * A001519(n)) / 10 = a(1 - n).

G.f.: (4 / (1 - x) + (1 - 6*x) / (1 - 7*x + x^2) + (5 - 10*x) / (1 - 3*x + x^2)) / 10.

a(0)=1, a(1)=1, a(2)=2, a(3)=7, a(4)=35, a(n)=11*a(n-1)-33*a(n-2)+ 33*a(n-3)- 11*a(n-4)+a(n-5). - Harvey P. Dale, Nov 18 2013

a(n) = a(1-n) for all n in Z. - Michael Somos, Sep 22 2014

0 = a(n)*(+a(n+1) + 4*a(n+2)) + a(n+1)*(-11*a(n+1) + a(n+2)) for all n in Z. - Michael Somos, Sep 22 2014

a(n) = b(n+1) * b(n) * b(n-1) * b(n-2) / 6 for all n in Z where b = A005247. - Michael Somos, Sep 22 2014

EXAMPLE

G.f. = 1 + x + 2*x^2 + 7*x^3 + 35*x^4 + 210*x^5 + 1365*x^6 + 9165*x^7 + ...

MATHEMATICA

RecurrenceTable[{a[0]==a[1]==1, a[n]==a[n-1] (11a[n-1]-a[n-2])/(a[n-1]+ 4a[n-2])}, a, {n, 30}] (* or *) LinearRecurrence[{11, -33, 33, -11, 1}, {1, 1, 2, 7, 35}, 30] (* Harvey P. Dale, Nov 18 2013 *)

PROG

(PARI) {a(n) = (4 + fibonacci(4*n - 1)/3 + fibonacci(4*n - 3)/3 + 5 * fibonacci(2*n - 1)) / 10};

(PARI) {a(n) = my(A); if( n<1, n = 1-n); if( n<3, n, A = vector(n, k, k); for(k=3, n, A[k] = A[k-1] * (11*A[k-1] - A[k-2]) / (A[k-1] + 4*A[k-2])); A[n])}; /* Michael Somos, Sep 22 2014 */

CROSSREFS

Cf. A005247.

Sequence in context: A020066 A024719 A086637 * A214461 A130458 A003575

Adjacent sequences:  A172508 A172509 A172510 * A172512 A172513 A172514

KEYWORD

nonn

AUTHOR

Michael Somos, Feb 05 2010

STATUS

approved

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Last modified May 28 04:02 EDT 2022. Contains 354112 sequences. (Running on oeis4.)