A301693 - OEIS

%I #22 Jul 31 2024 11:16:58

%S 1,5,12,21,33,49,70,95,121,150,184,222,263,305,351,403,458,515,573,

%T 636,706,778,851,925,1005,1093,1182,1271,1361,1458,1564,1670,1775,

%U 1881,1995,2119,2242,2363,2485,2616,2758,2898,3035,3173,3321,3481,3638,3791,3945,4110,4288,4462,4631,4801,4983,5179,5370,5555,5741,5940,6154,6362,6563,6765,6981,7213,7438,7655,7873,8106,8356,8598,8831,9065,9315,9583,9842,10091,10341,10608,10894,11170,11435,11701,11985,12289,12582,12863,13145,13446,13768,14078,14375,14673,14991,15331,15658,15971,16285,16620,16978

%N Partial sums of A301692.

%C Linear recurrence and g.f. confirmed by Shutov/Maleev link in A301692. - _Ray Chandler_, Aug 30 2023

%H Ray Chandler, <a href="/A301693/b301693.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 (1,0,0,0,2,-2,0,0,0,-1,1).

%F From _Colin Barker_, Apr 07 2018: (Start)

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

%F a(n) = a(n-1) + 2*a(n-5) - 2*a(n-6) - a(n-10) + a(n-11) for n>13. (End)

%t LinearRecurrence[{1, 0, 0, 0, 2, -2, 0, 0, 0, -1, 1}, {1, 5, 12, 21, 33, 49, 70, 95, 121, 150, 184, 222, 263, 305}, 100] (* _Paolo Xausa_, Jul 31 2024 *)

%Y Cf. A301692.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Mar 25 2018