OFFSET
0,4
COMMENTS
The general Somos-6 sequence terms s(n), with general coefficients and initial values s(0)..s(5), are Laurent polynomials with denominators a product of initial values raised to powers being entries in this sequence. Thus, the denominator of s(n) = Product_{k=0..5} s(k)^a(n-k-6). - Michael Somos, Apr 10 2020
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
FORMULA
a(n) = 1 + floor( n*(n+13)/42 ).
From Michael Somos, Apr 10 2020: (Start)
G.f.: (1-x+x^3-x^4+x^5-x^6+x^7-x^9+x^10)/((1-x)^2*(1-x^21)).
a(n) = a(-13-n).
a(n) = a(n-21) + n + 4 for all n in Z.
0 = +a(n)*(a(n+1) -a(n+3) -a(n+4) +a(n+6)) + a(n+1)*(-a(n+1) +a(n+3) +a(n+4) -a(n+5)) + a(n+2)*(-a(n+3) +a(n+4) +a(n+5) -a(n+6)) + a(n+3)*(+a(n+3) -a(n+5) +a(n+6) -a(n+6)) + a(n+5)*(-a(n+5) +a(n+6)) for all n in Z. (End)
a(n) = floor(binomial(n+7,2)/21). - G. C. Greubel, Mar 23 2023
EXAMPLE
G.f. = 1 + x + x^2 + 2*x^3 + 2*x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + ... - Michael Somos, Apr 10 2020
MATHEMATICA
a[n_]:= Quotient[n(n+13), 42] + 1; (* Michael Somos, Apr 10 2020 *)
Floor[Binomial[Range[0, 100]+7, 2]/21] (* G. C. Greubel, Mar 23 2023 *)
PROG
(PARI) {a(n) = n*(n + 13)\42 + 1}; /* Michael Somos, Apr 10 2020 */
(Magma) [Floor(Binomial(n+7, 2)/21): n in [0..80]]; // G. C. Greubel, Mar 23 2023
(SageMath) [binomial(n+7, 2)//21 for n in range(81)] # G. C. Greubel, Mar 23 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 01 2003
STATUS
approved