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A131355 Partial sums of A065423 plus one.

%I A131355 #25 May 28 2025 15:42:33
%S A131355 1,1,1,3,4,8,10,16,19,27,31,41,46,58,64,78,85,101,109,127,136,156,166,
%T A131355 188,199,223,235,261,274,302,316,346,361,393,409,443,460,496,514,552,
%U A131355 571,611,631,673,694,738,760,806,829,877,901,951,976,1028,1054,1108
%N A131355 Partial sums of A065423 plus one.
%C A131355 Number of 132-avoiding even Grassmannian permutations of size n. - _Juan B. Gil_, Mar 10 2023
%H A131355 Juan B. Gil and Jessica A. Tomasko, <a href="https://arxiv.org/abs/2207.12617">Pattern-avoiding even and odd Grassmannian permutations</a>, arXiv:2207.12617 [math.CO], 2022.
%H A131355 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A131355 From _R. J. Mathar_, Jul 17 2009: (Start)
%F A131355 G.f.: (1 - 2*x^2 + 2*x^3 + 2*x^4)/((1+x)^2*(1-x)^3).
%F A131355 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), n > 5. (End)
%F A131355 a(n) = (6*n^2 - 10*n + 17 - (1+2n)*(-1)^n)/16. - _Wesley Ivan Hurt_, Jul 28 2015
%F A131355 a(n) = 1 + binomial(n,2) - binomial(floor(n/2)+1,2). - _Juan B. Gil_, Mar 10 2023
%p A131355 A065423 := proc(n) if n mod 2 <> 0 then n-1 ; else n/2-1 ; fi ; end: A131355 := proc(n) 1+add(A065423(i), i=1..n) ; end: seq(A131355(n),n=0..80) ; # _R. J. Mathar_, Oct 04 2007
%t A131355 Table[(6 n^2 - 10 n + 17 - (1 + 2 n) (-1)^n)/16, {n, 0, 100}] (* _Wesley Ivan Hurt_, Jul 28 2015 *)
%t A131355 LinearRecurrence[{1, 2, -2, -1, 1}, {1, 1, 1, 3, 4}, 70] (* _Vincenzo Librandi_, Jul 29 2015 *)
%t A131355 Join[{1},Accumulate[LinearRecurrence[{0,2,0,-1},{0,0,2,1},100]]+1] (* _Harvey P. Dale_, May 28 2025 *)
%o A131355 (Magma) [(6*n^2-10*n+17-(1+2*n)*(-1)^n)/16: n in [0..70]]; // _Vincenzo Librandi_, Jul 29 2015
%Y A131355 Cf. A065423.
%K A131355 nonn,easy
%O A131355 0,4
%A A131355 _Paul Curtz_, Sep 30 2007
%E A131355 More terms from _R. J. Mathar_, Oct 04 2007