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 A265078 Partial sums of A072154. 2

%I #10 Sep 08 2022 08:46:14

%S 1,4,9,16,25,37,52,69,88,109,133,160,189,220,253,289,328,369,412,457,

%T 505,556,609,664,721,781,844,909,976,1045,1117,1192,1269,1348,1429,

%U 1513,1600,1689,1780,1873,1969,2068,2169,2272,2377,2485,2596,2709,2824,2941,3061,3184,3309,3436,3565,3697

%N Partial sums of A072154.

%H Colin Barker, <a href="/A265078/b265078.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).

%F G.f.: (1+x)^2*(1-x+x^2)*(1+x+x^2) / ((1-x)^3*(1+x+x^2+x^3+x^4)).

%F a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7). - _Vincenzo Librandi_, Jan 01 2016

%t LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {1, 4, 9, 16, 25, 37, 52}, 60] (* _Vincenzo Librandi_, Jan 01 2016 *)

%o (PARI) Vec((1+x)^2*(1-x+x^2)*(1+x+x^2)/((1-x)^3*(1+x+x^2+x^3+x^4)) + O(x^70)) \\ _Colin Barker_, Jan 01 2016

%o (Magma) I:=[1,4,9,16,25,37,52]; [n le 7 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-5)-2*Self(n-6)+Self(n-7): n in [1..60]]; // _Vincenzo Librandi_, Jan 01 2016

%Y Cf. A072154.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 29 2015

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Last modified September 13 10:55 EDT 2024. Contains 375904 sequences. (Running on oeis4.)