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%I #25 May 22 2024 02:13:43
%S 0,1,7,33,139,565,2271,9097,36403,145629,582535,2330161,9320667,
%T 37282693,149130799,596523225,2386092931,9544371757,38177487063,
%U 152709948289,610839793195,2443359172821,9773436691327,39093746765353,156374987061459,625499948245885,2501999792983591
%N a(n) = 4*a(n-1) + 2*n - 1.
%H Stefano Spezia, <a href="/A141291/b141291.txt">Table of n, a(n) for n = 0..1500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).
%F a(n) = 4*a(n-1) + 2*n-1, given a(0) = 0, a(1) = 1.
%F Row sums of triangle A141290 starting with offset 1.
%F From _R. J. Mathar_, Feb 02 2010: (Start)
%F a(n) = 6*a(n-1) -9*a(n-2) +4*a(n-3).
%F G.f.: x*(1+x)/((1-4*x)*(x-1)^2). (End)
%F E.g.f.: exp(x)*(5*(exp(3*x) - 1) - 6*x) /9. - _Stefano Spezia_, May 21 2024
%e a(4) = 139 = 4*a(3) + 7 = 4*33 + 7.
%e a(4) = 139 = sum of row 4 terms of triangle A141290 = (64, + 48 + 20 + 7).
%t LinearRecurrence[{6,-9,4},{0,1,7},27] (* _Stefano Spezia_, May 21 2024 *)
%Y Cf. A141290.
%K nonn,easy
%O 0,3
%A _Gary W. Adamson_, Jun 22 2008
%E Definition and formula corrected by _Paolo P. Lava_, Oct 07 2008
%E More terms from _R. J. Mathar_, Feb 02 2010
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