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

%I #15 Jun 25 2021 17:21:45

%S 1,12,57,160,345,636,1057,1632,2385,3340,4521,5952,7657,9660,11985,

%T 14656,17697,21132,24985,29280,34041,39292,45057,51360,58225,65676,

%U 73737,82432,91785,101820,112561,124032,136257,149260,163065,177696,193177,209532,226785,244960,264081

%N a(n) = 4*n^3 + 5*n^2 + 2*n + 1.

%H Andrew Howroyd, <a href="/A204674/b204674.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 a(n) = (4*n^2 + n + 1) * (n + 1).

%F G.f.: (1 + 3*x)*(1 + 5*x)/(1 - x)^4. - _Andrew Howroyd_, Jan 07 2020

%t LinearRecurrence[{4,-6,4,-1},{1,12,57,160},50] (* or *) CoefficientList[ Series[(1+3x)(1+5x)/(1-x)^4,{x,0,50}],x] (* _Harvey P. Dale_, Jun 25 2021 *)

%o (Haskell)

%o a204674 n = n * (n * (4 * n + 5) + 2) + 1

%o (PARI) a(n)={ 4*n^3 + 5*n^2 + 2*n + 1 } \\ _Andrew Howroyd_, Jan 07 2020

%Y Row sums of A033293.

%Y Cf. A054567, A226449.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, Jan 18 2012

%E Terms a(26) and beyond from _Andrew Howroyd_, Jan 07 2020