This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A301725 #19 Aug 30 2023 13:40:19 %S A301725 1,7,17,33,56,83,114,152,196,244,298,358,422,492,569,650,735,827,925, %T A301725 1027,1135,1249,1367,1491,1622,1757,1896,2042,2194,2350,2512,2680, %U A301725 2852,3030,3215,3404,3597,3797,4003,4213,4429,4651,4877,5109,5348,5591,5838,6092,6352 %N A301725 Partial sums of A301724. %C A301725 Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301724. - _Ray Chandler_, Aug 30 2023 %H A301725 Ray Chandler, <a href="/A301725/b301725.txt">Table of n, a(n) for n = 0..1000</a> %H A301725 <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 A301725 From _Colin Barker_, Apr 06 2018: (Start) %F A301725 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 A301725 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 A301725 (End) %t A301725 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 A301725 Cf. A301724. %K A301725 nonn %O A301725 0,2 %A A301725 _N. J. A. Sloane_, Mar 26 2018