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%I #23 Dec 26 2022 12:06:32
%S 1,26,98,238,467,806,1276,1898,2693,3682,4886,6326,8023,9998,12272,
%T 14866,17801,21098,24778,28862,33371,38326,43748,49658,56077,63026,
%U 70526,78598,87263,96542,106456
%N 1 + (26*n+17+7*n^2)*n/2.
%C Multiply the n-th power of the 4 X 4 matrix [1 0 0 0 / 1 1 0 0 / 2 3 1 0 / 6 12 7 1] by the column vector [1 1 1 1] from the right. Then a(n) is the last component of the vector that results, and A095794(n) the penultimate component.
%H Vincenzo Librandi, <a href="/A095796/b095796.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*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4).
%F G.f. ( 1+22*x-2*x^3 ) / (x-1)^4 . - R. J. Mathar, Nov 05 2011
%e 806 = a(5) since M65 * [1 1 1 1] = [1 6 56 806] where 56 = A095794(5).
%t LinearRecurrence[{4,-6, 4,-1},{1,26,98,238},40] (* _Vincenzo Librandi_, Jun 24 2012 *)
%t Table[1+(26n+17+7n^2)n/2,{n,0,30}] (* or *) CoefficientList[Series[ (1+ 22x- 2x^3)/(-1+x)^4,{x,0,30}],x]
%o (Magma) I:=[1, 26, 98, 238]; [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_, Jun 24 2012
%Y Cf. A095794.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_, Jun 06 2004
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