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A217776 a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5) + (n+6)*(n+7).

%I A217776 #22 Sep 08 2022 08:46:04
%S A217776 68,100,140,188,244,308,380,460,548,644,748,860,980,1108,1244,1388,
%T A217776 1540,1700,1868,2044,2228,2420,2620,2828,3044,3268,3500,3740,3988,
%U A217776 4244,4508,4780,5060,5348,5644,5948,6260,6580,6908,7244,7588,7940,8300,8668,9044,9428
%N A217776 a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5) + (n+6)*(n+7).
%H A217776 G. C. Greubel, <a href="/A217776/b217776.txt">Table of n, a(n) for n = 0..1000</a>
%H A217776 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A217776 From _Bruno Berselli_, Mar 29 2013: (Start)
%F A217776 G.f.: 4*(17-26*x+11*x^2)/(1-x)^3.
%F A217776 a(n) = 4*n^2 + 28*n + 68.
%F A217776 a(n) = 4*A027690(n+3) = A020742(n)^2 + 19. (End)
%F A217776 E.g.f.: 4*(17 +8*x +x^2)*exp(x). - _G. C. Greubel_, Aug 27 2019
%e A217776 a(1) = 1*2 + 3*4 + 5*6 + 7*8 = 2 + 12 + 30 + 56 = 100.
%p A217776 seq((2*n+7)^2+19, n=0..50); # _G. C. Greubel_, Aug 27 2019
%t A217776 (2*Range[50] +5)^2 +19 (* _G. C. Greubel_, Aug 27 2019 *)
%t A217776 Table[4n^2+28n+68,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{68,100,140},50] (* _Harvey P. Dale_, Jan 15 2020 *)
%o A217776 (JavaScript)
%o A217776 for (j=0;j<50;j++) {
%o A217776 a=j*(j+1)+(j+2)*(j+3)+(j+4)*(j+5)+(j+6)*(j+7);
%o A217776 document.write(a+", ");
%o A217776 }
%o A217776 (PARI) a(n)=4*n^2+28*n+68 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A217776 (Magma) [(2*n+7)^2+19: n in [0..50]]; // _G. C. Greubel_, Aug 27 2019
%o A217776 (Sage) [(2*n+7)^2+19 for n in (0..50)] # _G. C. Greubel_, Aug 27 2019
%o A217776 (GAP) List([0..50], n-> (2*n+7)^2+19); # _G. C. Greubel_, Aug 27 2019
%Y A217776 Cf. A020742, A027690, A051890 (two pairs), A217775 (3 pairs).
%K A217776 nonn,easy
%O A217776 0,1
%A A217776 _Jon Perry_, Mar 24 2013