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A356288 Sum of numbers in n-th upward diagonal of triangle the sum of {1; 2,3; 4,5,6; 7,8,9,10; ...} and {1; 2,3; 3,4,5; 4,5,6,7; ...}.

%I A356288 #31 Oct 05 2022 04:55:02
%S A356288 2,4,13,20,40,55,90,116,170,210,287,344,448,525,660,760,930,1056,1265,
%T A356288 1420,1672,1859,2158,2380,2730,2990,3395,3696,4160,4505,5032,5424,
%U A356288 6018,6460,7125,7620,8360,8911,9730,10340,11242,11914,12903,13640,14720,15525,16700
%N A356288 Sum of numbers in n-th upward diagonal of triangle the sum of {1; 2,3; 4,5,6; 7,8,9,10; ...} and {1; 2,3; 3,4,5; 4,5,6,7; ...}.
%H A356288 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F A356288 a(n) = (n * ceiling(n/2)) + ((15 + 25*n + 15*n^2 + 14*n^3 - 3*(((-1)^n))*(5 + n*(3 + n))) / 96).
%F A356288 a(n) = A079824(n) + A093005(n).
%F A356288 G.f.: x*(2 + 2*x + 3*x^2 + x^3 - x^4)/((1 - x)^4*(1 + x)^3). - _Stefano Spezia_, Aug 19 2022
%e A356288    2 = A079824(1) + A093005(1) =  1 + 1.
%e A356288    4 = A079824(2) + A093005(2) =  2 + 2.
%e A356288   13 = A079824(3) + A093005(3) =  7 + 6.
%e A356288   20 = A079824(4) + A093005(4) = 12 + 8.
%o A356288 (Python)
%o A356288 def a(n): return (n * ((n + n % 2) // 2)) + (15 + 25*n + 15*(n**2) + 14*(n**3) - 3*(((-1)**n))*(5 + n*(3 + n))) // 96
%Y A356288 Cf. A079824, A093005.
%K A356288 nonn,easy
%O A356288 1,1
%A A356288 _Torlach Rush_, Aug 02 2022