A301727 - OEIS

%I #20 Aug 30 2023 13:43:58

%S 1,6,17,33,54,81,114,152,195,244,298,357,422,492,567,648,735,827,924,

%T 1027,1135,1248,1367,1491,1620,1755,1896,2042,2193,2350,2512,2679,

%U 2852,3030,3213,3402,3597,3797,4002,4213,4429,4650,4877,5109,5346,5589,5838,6092,6351,6616,6886,7161,7442,7728,8019,8316,8619,8927

%N Partial sums of A301726.

%C Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301726. - _Ray Chandler_, Aug 30 2023

%H Ray Chandler, <a href="/A301727/b301727.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3, -4, 4, -4, 4, -4, 4, -4, 4, -3, 1).

%F From _Colin Barker_, Apr 09 2018: (Start)

%F G.f.: (1 + x + x^2)*(1 + 2*x + 3*x^4 + 2*x^7 + x^8) / ((1 - x)^3*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).

%F a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 4*a(n-4) + 4*a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 4*a(n-9) - 3*a(n-10) + a(n-11) for n>10.

%F (End)

%t Accumulate[CoefficientList[Series[(x^2+x+1)(x^8+2x^7+3x^4+2x+1)/ ((x^4+ x^3+x^2+x+1)(x^4-x^3+x^2-x+1)(x-1)^2),{x,0,110}],x]] (* _Harvey P. Dale_, Sep 25 2020 *)

%Y Cf. A301726.

%K nonn

%O 0,2

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