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A353099 a(1) = 7; for n>1, a(n) = 8 * a(n-1) + 8 - n.

%I A353099 #25 May 29 2023 07:13:10
%S A353099 7,62,501,4012,32099,256794,2054353,16434824,131478591,1051828726,
%T A353099 8414629805,67317038436,538536307483,4308290459858,34466323678857,
%U A353099 275730589430848,2205844715446775,17646757723574190,141174061788593509,1129392494308748060
%N A353099 a(1) = 7; for n>1, a(n) = 8 * a(n-1) + 8 - n.
%H A353099 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-17,8).
%F A353099 G.f.: x * (7 - 8 * x)/((1 - x)^2 * (1 - 8 * x)).
%F A353099 a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3).
%F A353099 a(n) = 6 * A014831(n) + n.
%F A353099 a(n) = (6*8^(n+1) + 7*n - 48)/49.
%F A353099 a(n) = Sum_{k=0..n-1} (8 - n + k)*8^k.
%F A353099 E.g.f.: exp(x)*(48*(exp(7*x) - 1) + 7*x)/49. - _Stefano Spezia_, May 29 2023
%t A353099 LinearRecurrence[{10, -17, 8}, {7, 62, 501}, 20] (* _Amiram Eldar_, Apr 23 2022 *)
%o A353099 (PARI) my(N=30, x='x+O('x^N)); Vec(x*(7-8*x)/((1-x)^2*(1-8*x)))
%o A353099 (PARI) a(n) = (6*8^(n+1)+7*n-48)/49;
%o A353099 (PARI) b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
%o A353099 a(n) = b(n, 8);
%Y A353099 Cf. A064617, A353094, A353095, A353096, A353097, A353098, A353100.
%Y A353099 Cf. A014831.
%K A353099 nonn,easy
%O A353099 1,1
%A A353099 _Seiichi Manyama_, Apr 23 2022