A301725 - OEIS

%I #19 Aug 30 2023 13:40:19

%S 1,7,17,33,56,83,114,152,196,244,298,358,422,492,569,650,735,827,925,

%T 1027,1135,1249,1367,1491,1622,1757,1896,2042,2194,2350,2512,2680,

%U 2852,3030,3215,3404,3597,3797,4003,4213,4429,4651,4877,5109,5348,5591,5838,6092,6352

%N Partial sums of A301724.

%C Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301724. - _Ray Chandler_, Aug 30 2023

%H Ray Chandler, <a href="/A301725/b301725.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 06 2018: (Start)

%F G.f.: (1 + 4*x + 6*x^3 + x^4 + 3*x^5 + x^6 + 6*x^7 + 4*x^9 + x^10) / ((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^10+4x^9+6x^7+x^6+3x^5+x^4+6x^3+4x+1)/ ((x^4+x^3+x^2+x+1)(x^4-x^3+x^2-x+1)(x-1)^2),{x,0,100}],x]] (* _Harvey P. Dale_, May 05 2022 *)

%Y Cf. A301724.

%K nonn

%O 0,2

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