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A227999 a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-4) + a(n-3)^2) / a(n-6), a(0) = a(1) = a(2) = a(3) = 1, a(4) = a(5) = 2. 1
1, 1, 1, 1, 2, 2, 5, 11, 25, 97, 220, 1396, 6053, 30467, 249431, 1381913, 19850884, 160799404, 1942868797, 36133524445, 458473480079, 13521902050025, 220176552243482, 7006033824529130, 276364333237297549, 7470025110120086101, 460097285931623600317, 17010560092754291510533, 1372227474279446678113082 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

David Speyer showed (modulo some empirical relations) that all terms are integer.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..172

MathOverflow, Does this sequence always give an integer?

FORMULA

For n>=6, a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-4) + a(n-3)^2) / a(n-6).

a(n) = a(3-n) for all n in Z. - Michael Somos, Apr 25 2017

0 = a(n)*a(n+9) +a(n+1)*a(n+8) +a(n+2)*a(n+7) -a(n+3)*a(n+6) -32*a(n+4)*a(n+5) for all n in Z. - Michael Somos, Apr 25 2017

0 = a(n)*a(n+10) -a(n+1)*a(n+9) -32*a(n+2)*a(n+8) +17*a(n+3)*a(n+7) +49*a(n+4)*a(n+6) for all n in Z. - Michael Somos, Apr 25 2017

0 = +a(n)*a(n+11) -32*a(n+1)*a(n+10) -33*a(n+2)*a(n+9) -49*a(n+3)*a(n+8) +1007*a(n+5)*a(n+6) for all n in Z. - Michael Somos, Apr 25 2017

MATHEMATICA

RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==1, a[4]==a[5]==2, a[n]==(a[n-1] a[n-5]+ a[n-2]a[n-4]+a[n-3]^2)/a[n-6]}, a, {n, 30}] (* Harvey P. Dale, Nov 11 2014 *)

a[ n_] := Which[ Abs[n - 3/2] < 2, 1, Abs[n - 3/2] < 4, 2, n < 0, a[3 - n], True, (a[n - 1] a[n - 5] + a[n - 2] a[n - 4] + a[n - 3]^2) / a[n - 6]]; (* Michael Somos, Jul 24 2018 *)

PROG

(PARI) {a(n) = my(v); if( n<2, n = 3-n); n++; v = vector(n, i, 1+(i>4)); for(k=7, n, v[k] = (v[k-1]*v[k-5] + v[k-2]*v[k-4] + v[k-3]*v[k-3]) / v[k-6]); v[n]}; /* Michael Somos, Apr 25 2017 */

(MAGMA) I:=[1, 1, 1, 1, 2, 2]; [n le 6 select I[n] else (Self(n-1)*Self(n-5) + Self(n-2)*Self(n-4) + Self(n-3)^2)/Self(n-6): n in [1..30]]; // G. C. Greubel, Aug 08 2018

CROSSREFS

A variation of A006722.

Sequence in context: A109278 A112527 A216642 * A049680 A153983 A262714

Adjacent sequences:  A227996 A227997 A227998 * A228000 A228001 A228002

KEYWORD

nonn

AUTHOR

Max Alekseyev, Dec 04 2013

STATUS

approved

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Last modified May 27 06:24 EDT 2019. Contains 323599 sequences. (Running on oeis4.)