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%I #12 Apr 07 2022 11:02:44
%S 1,1,11,12,113,125,1138,1263,11401,12664,114065,126729,1140794,
%T 1267523,11408317,12675840,114084157,126759997,1140844154,1267604151,
%U 11408448305,12676052456,114084500761,126760553217,1140845053978,1267605607195,11408450661173
%N Diagonal sum of generalized Pascal triangle; (10^n,1).
%H Robert Israel, <a href="/A164854/b164854.txt">Table of n, a(n) for n = 0..1990</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,11,-10,-10).
%F From _Robert Israel_, Jul 01 2016: (Start)
%F G.f.: (1-x^2)/((1-10*x^2)*(1-x-x^2)).
%F a(n) = (171-9*(-1)^n)*10^floor(n/2)/142 + (A000045(n)-10*A000045(n+2))/71. (End)
%F a(n) = a(n-1)+11*a(n-2)-10*a(n-3)-10*a(n-4). - _Wesley Ivan Hurt_, Apr 21 2021
%p f:= gfun:-rectoproc({10*a(n-4)+10*a(n-3)-11*a(n-2)-a(n-1)+a(n),
%p a(0)=1,a(1)=1,a(2)=11,a(3)=12},a(n),remember):
%p map(f, [$0..30]); # _Robert Israel_, Jul 01 2016
%t LinearRecurrence[{1,11,-10,-10},{1,1,11,12},30] (* _Harvey P. Dale_, Apr 07 2022 *)
%Y Cf. A164844, A164852, A000045.
%K nonn,easy
%O 0,3
%A _Mark Dols_, Aug 28 2009
%E More terms from _Harvey P. Dale_, Apr 07 2022