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A061349 Sum of antidiagonals of A060736.

%I A061349 #27 Jun 05 2023 09:29:36
%S A061349 0,1,6,17,40,75,130,203,304,429,590,781,1016,1287,1610,1975,2400,2873,
%T A061349 3414,4009,4680,5411,6226,7107,8080,9125,10270,11493,12824,14239,
%U A061349 15770,17391,19136,20977,22950,25025,27240,29563,32034,34619,37360,40221
%N A061349 Sum of antidiagonals of A060736.
%C A061349 a(1) = 1, a(2) = 2+4=6, a(3) = 5+3+9=17, a(4) = 10+6+8+16=40.
%H A061349 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-4,1,2,-1).
%F A061349 a(n) = A005900(n) - A006918(n).
%F A061349 a(n) = a(n-1) + A001844(n-1) - A002378(A004526(n-1)).
%F A061349 a(n) = a(n-1) + n^2 + (n - 1)^2 - floor((n-1)/2)*floor((n+1)/2).
%F A061349 If n is odd then a(n) = (7*n^3 + 5*n)/12;
%F A061349 If n is even then a(n) = (7*n^3 + 8*n)/12.
%F A061349 From _Colin Barker_, Sep 13 2014: (Start)
%F A061349 a(n) = (n*(13 + 3*(-1)^n + 14*n^2))/24.
%F A061349 a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
%F A061349 G.f.: x*(x^4 + 4*x^3 + 4*x^2 + 4*x + 1)/((x - 1)^4*(x + 1)^2). (End)
%F A061349 E.g.f.: x*((12 + 21*x + 7*x^2)*cosh(x) + (15 + 21*x + 7*x^2)*sinh(x))/12. - _Stefano Spezia_, Jun 05 2023
%t A061349 LinearRecurrence[{2,1,-4,1,2,-1},{0,1,6,17,40,75},50] (* _Harvey P. Dale_, Oct 17 2021 *)
%t A061349 Accumulate[Table[n^2 + (n - 1)^2 - Floor[((n-1)/2)]*Floor[((n+1)/2)],{n,41}]] (* _Stefano Spezia_, Jun 05 2023 *)
%o A061349 (PARI) concat(0, Vec(x*(x^4+4*x^3+4*x^2+4*x+1)/((x-1)^4*(x+1)^2) + O(x^100))) \\ _Colin Barker_, Sep 13 2014
%Y A061349 Cf. A001844, A002378, A004526, A005900, A006918, A060736.
%K A061349 nonn,easy
%O A061349 0,3
%A A061349 _Henry Bottomley_, Jun 07 2001