A055803 - OEIS

%I #17 Jan 28 2023 11:29:18

%S 1,1,1,2,3,5,7,11,14,21,25,36,41,57,63,85,92,121,129,166,175,221,231,

%T 287,298,365,377,456,469,561,575,681,696,817,833,970,987,1141,1159,

%U 1331,1350,1541,1561,1772,1793,2025,2047,2301

%N a(n) = T(n,n-3), array T as in A055801.

%C Third differences seem to be A002620(n)+1.

%H G. C. Greubel, <a href="/A055803/b055803.txt">Table of n, a(n) for n = 3..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).

%F From _Colin Barker_, Nov 28 2014: (Start)

%F a(n) = (-39 +55*n -15*n^2 +2*n^3 +(-1)^n*(135 -39*n +3*n^2))/96 for n>3.

%F G.f.: x^3*(1 -3*x^2 +x^3 +4*x^4 -x^5 -2*x^6 +x^7)/((1-x)^4*(1+x)^3). (End)

%F E.g.f.: ( 8*(x^3 -3*x^2 +6*x -6) +(x^3 -3*x^2 +39*x +48)*cosh(x) +(x^3 -6*x^2 +3*x -87)*sinh(x) )/48. - _G. C. Greubel_, Jan 23 2020

%p seq( `if`(n=3, 1, (-39 +55*n -15*n^2 +2*n^3 +(-1)^n*(135 -39*n +3*n^2))/96), n=3..60); # _G. C. Greubel_, Jan 23 2020

%t Table[If[n==3, 1, (-39 +55*n -15*n^2 +2*n^3 +(-1)^n*(135 -39*n +3*n^2))/96], {n,3,60}] (* _G. C. Greubel_, Jan 23 2020 *)

%t LinearRecurrence[{1,3,-3,-3,3,1,-1},{1,1,1,2,3,5,7,11},50] (* _Harvey P. Dale_, Jan 28 2023 *)

%o (PARI) vector(60, n, my(m=n+2); if(m==3, 1, (-39 +55*m -15*m^2 +2*m^3 +(-1)^m*(135 -39*m +3*m^2))/96)) \\ _G. C. Greubel_, Jan 23 2020

%o (Magma) [1] cat [(-39 +55*n -15*n^2 +2*n^3 +(-1)^n*(135 -39*n +3*n^2))/96: n in [4..60]]; // _G. C. Greubel_, Jan 23 2020

%o (Sage) [1]+[(-39 +55*n -15*n^2 +2*n^3 +(-1)^n*(135 -39*n +3*n^2))/96 for n in (4..60)] # _G. C. Greubel_, Jan 23 2020

%o (GAP) Concatenation([1], List([4..60], n-> (-39 +55*n -15*n^2 +2*n^3 +(-1)^n*(135 -39*n +3*n^2))/96 )); # _G. C. Greubel_, Jan 23 2020

%Y Cf. A055801, A055802, A055804, A055805, A055806.

%K nonn

%O 3,4

%A _Clark Kimberling_, May 28 2000