A077169 - OEIS

%I #16 Dec 13 2022 02:14:15

%S 1,2,4,7,11,15,20,26,33,41,50,60,71,83,96,110,125,141,158,176,195,215,

%T 236,258,281,305,330,356,383,411,440,470,501,533,566,600,635,671,708,

%U 746,785,825,866,908,951,995,1040,1086,1133,1181,1230,1280,1331,1383

%N Initial terms of rows of A077168.

%H G. C. Greubel, <a href="/A077169/b077169.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F For n>3, a(n) = (n^2-n+10)/2.

%F From _G. C. Greubel_, Jul 13 2017: (Start)

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n >= 7.

%F G.f.: (1-x+x^2-x^5 + x^6)/(1-x)^3.

%F E.g.f.: (1/2)*(x^2 + 10)*exp(x) - 4 - 3*x + x^2 - x^3/6. (End)

%F Sum_{n>=0} 1/a(n) = 1177/840 + 2*Pi*tanh(sqrt(39)*Pi/2)/sqrt(39). - _Amiram Eldar_, Dec 13 2022

%t Join[{1, 2, 4, 7}, Table[(n^2 - n + 10)/2, {n, 4, 50}]] (* _G. C. Greubel_, Jul 13 2017 *)

%o (PARI) concat([1,2,4,7], for(n=4,50, print1((n^2 - n +10)/2, ", "))) \\ _G. C. Greubel_, Jul 13 2017

%Y Cf. A077168, A077170.

%K nonn,easy

%O 0,2

%A _Amarnath Murthy_, Nov 01 2002

%E More terms from _Sascha Kurz_, Feb 10 2003