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A084630 Floor(C(n+7,7)/C(n+5,5)). 0
1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 22, 23, 25, 26, 28, 30, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 56, 58, 60, 63, 65, 68, 70, 73, 76, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 115, 118, 121, 125, 128, 132, 135 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..69.

FORMULA

a(n)=floor(n^2/42+13n/42)+1.

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-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)

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 *)

PROG

(PARI) {a(n) = n*(n + 13)\42 + 1}; /* Michael Somos, Apr 10 2020 */

CROSSREFS

Cf. A084629.

Sequence in context: A213856 A173329 A241951 * A325393 A320388 A264396

Adjacent sequences:  A084627 A084628 A084629 * A084631 A084632 A084633

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 01 2003

STATUS

approved

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Last modified February 26 03:10 EST 2021. Contains 341619 sequences. (Running on oeis4.)