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A226451 a(n) = n*(7*n^2-12*n+7)/2. 3

%I

%S 0,1,11,51,142,305,561,931,1436,2097,2935,3971,5226,6721,8477,10515,

%T 12856,15521,18531,21907,25670,29841,34441,39491,45012,51025,57551,

%U 64611,72226,80417,89205,98611,108656,119361,130747,142835,155646,169201,183521

%N a(n) = n*(7*n^2-12*n+7)/2.

%C See the comment in A226449.

%H Bruno Berselli, <a href="/A226451/b226451.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: x*(1+7*x+13*x^2)/(1-x)^4.

%F a(n) = A001106(n) + n*A001106(n-1).

%t Table[n (7 n^2 - 12 n + 7)/2, {n, 0, 40}]

%t CoefficientList[Series[x (1 + 7 x + 13 x^2)/(1 - x)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 18 2013 *)

%o (MAGMA) [n*(7*n^2-12*n+7)/2: n in [0..40]];

%o (MAGMA) I:=[0,1,11,51]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Aug 18 2013

%Y Cf. A001106.

%Y Similar sequences of the type b(m)+m*b(m-1), where b is a polygonal number: A006003, A069778, A143690, A204674, A212133, A226449, A226450.

%K nonn,easy

%O 0,3

%A _Bruno Berselli_, Jun 07 2013

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Last modified May 17 12:55 EDT 2021. Contains 343971 sequences. (Running on oeis4.)