cp's OEIS Frontend

A316466 a(n) = 2*n*(7*n - 3).

%I A316466 #28 Sep 08 2022 08:46:22
%S A316466 0,8,44,108,200,320,468,644,848,1080,1340,1628,1944,2288,2660,3060,
%T A316466 3488,3944,4428,4940,5480,6048,6644,7268,7920,8600,9308,10044,10808,
%U A316466 11600,12420,13268,14144,15048,15980,16940,17928,18944,19988,21060,22160,23288,24444,25628,26840
%N A316466 a(n) = 2*n*(7*n - 3).
%C A316466 This is the case k = 9 of Sum_{i = 2..k} P(i,n) = (k - 1)*n*((k - 2)*n - (k - 6))/4, where P(k,n) = n*((k - 2)*n - (k - 4))/2 (see Crossrefs for similar sequences and "Square array in A139600" in Links section).
%C A316466 14*x + 9 is a square for x = a(n) or x = a(-n).
%H A316466 Colin Barker, <a href="/A316466/b316466.txt">Table of n, a(n) for n = 0..1000</a>
%H A316466 Bruno Berselli, <a href="/A316466/a316466.jpg">Square array in A139600</a>.
%H A316466 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A316466 O.g.f.: 4*x*(2 + 5*x)/(1 - x)^3.
%F A316466 E.g.f.: 2*x*(4 + 7*x)*exp(x).
%F A316466 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A316466 a(n) = 4*A218471(n).
%t A316466 Table[2 n (7 n - 3), {n, 0, 50}]
%t A316466 LinearRecurrence[{3,-3,1},{0,8,44},50] (* _Harvey P. Dale_, Jan 24 2021 *)
%o A316466 (PARI) vector(50, n, n--; 2*n*(7*n-3))
%o A316466 (PARI) concat(0, Vec(4*x*(2 + 5*x)/(1 - x)^3 + O(x^40))) \\ _Colin Barker_, Jul 05 2018
%o A316466 (Sage) [2*n*(7*n-3) for n in (0..50)]
%o A316466 (Maxima) makelist(2*n*(7*n-3), n, 0, 50);
%o A316466 (GAP) List([0..50], n -> 2*n*(7*n-3));
%o A316466 (Magma) [2*n*(7*n-3): n in [0..50]];
%o A316466 (Python) [2*n*(7*n-3) for n in range(50)]
%o A316466 (Julia) [2*n*(7*n-3) for n in 0:50] |> println
%Y A316466 Cf. A139600, A218471.
%Y A316466 Similar sequences (see the first comment): A000096 (k = 3), A045943 (k = 4), A049451 (k = 5), A033429 (k = 6), A167469 (k = 7), A152744 (k = 8), this sequence (k = 9), A152994 (k = 10).
%K A316466 nonn,easy
%O A316466 0,2
%A A316466 _Bruno Berselli_, Jul 04 2018