A298787 - OEIS

%I #21 Feb 24 2026 17:23:11

%S 1,4,11,21,34,51,71,94,121,151,184,221,261,304,351,401,454,511,571,

%T 634,701,771,844,921,1001,1084,1171,1261,1354,1451,1551,1654,1761,

%U 1871,1984,2101,2221,2344,2471,2601,2734,2871,3011,3154,3301,3451,3604,3761,3921,4084,4251,4421,4594,4771

%N Partial sums of A298786.

%H Colin Barker, <a href="/A298787/b298787.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

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

%F a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5) for n>4. - _Colin Barker_, Jan 27 2018

%F From _Stefano Spezia_, Apr 06 2023: (Start)

%F a(n) = (8 + 15*n + 15*n^2 + A061347(n+2))/9.

%F E.g.f.: exp(-x/2)*(exp(3*x/2)*(8 + 30*x + 15*x^2) + cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2))/9. (End)

%t LinearRecurrence[{2, -1, 1, -2, 1}, {1, 4, 11, 21, 34}, 50] (* _Paolo Xausa_, Feb 24 2026 *)

%o (PARI) Vec((1 + 2*x + 4*x^2 + 2*x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)) + O(x^60)) \\ _Colin Barker_, Jan 27 2018

%Y Cf. A061347, A298786.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jan 26 2018