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%I #12 Mar 24 2023 10:40:16
%S 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,
%T 26,28,30,31,33,35,37,39,41,43,45,47,49,51,53,56,58,60,63,65,68,70,73,
%U 76,78,81,84,87,90,93,96,99,102,105,108,111,115,118,121,125,128,132,135
%N a(n) = floor(C(n+7,7)/C(n+5,5)).
%C 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
%H G. C. Greubel, <a href="/A084630/b084630.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) = 1 + floor( n*(n+13)/42 ).
%F From _Michael Somos_, Apr 10 2020: (Start)
%F G.f.: (1-x+x^3-x^4+x^5-x^6+x^7-x^9+x^10)/((1-x)^2*(1-x^21)).
%F a(n) = a(-13-n).
%F a(n) = a(n-21) + n + 4 for all n in Z.
%F 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)
%F a(n) = floor(binomial(n+7,2)/21). - _G. C. Greubel_, Mar 23 2023
%e 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
%t a[n_]:= Quotient[n(n+13), 42] + 1; (* _Michael Somos_, Apr 10 2020 *)
%t Floor[Binomial[Range[0,100]+7,2]/21] (* _G. C. Greubel_, Mar 23 2023 *)
%o (PARI) {a(n) = n*(n + 13)\42 + 1}; /* _Michael Somos_, Apr 10 2020 */
%o (Magma) [Floor(Binomial(n+7,2)/21): n in [0..80]]; // _G. C. Greubel_, Mar 23 2023
%o (SageMath) [binomial(n+7,2)//21 for n in range(81)] # _G. C. Greubel_, Mar 23 2023
%Y Cf. A084628, A084631.
%K easy,nonn
%O 0,4
%A _Paul Barry_, Jun 01 2003
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