A116996 - OEIS

%I #15 Feb 25 2016 11:38:05

%S 0,1,4,6,10,15,22,28,36,45,56,66,78,91,106,120,136,153,172,190,210,

%T 231,254,276,300,325,352,378,406,435,466,496,528,561,596,630,666,703,

%U 742,780,820,861,904,946,990,1035,1082,1128,1176,1225

%N Partial sums of A116966.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,1,-2,1).

%F a(n) = SUM[i=1..n] A116966(n). a(n) = SUM[i=1..n] (n + {1,2,0,1} according as n == {0,1,2,3} mod 4). a(n) = A000217(n) = n*(n+1)/2 unless n == 2 mod 4 in which case a(n) = A000217(n)+1 = (n*(n+1)/2)+1.

%F G.f.: -x*(2*x^3-x^2+2*x+1) / ((x-1)^3*(x+1)*(x^2+1)). - _Colin Barker_, Apr 30 2013

%e a(1) = 1 = A000217(1).

%e a(2) = 1+3 = 4 = A000217(2)+1.

%e a(3) = 1+3+2 = 6 = A000217(3).

%e a(4) = 1+3+2+4 = 10 = A000217(4).

%e a(5) = 1+3+2+4+5 = 15 = A000217(5).

%e a(6) = 1+3+2+4+5+7 = 22 = A000217(6)+1.

%e a(27) = 1+3+2+4+5+7+6+8+9+11+10+12+13+15+14+16+17+19+18+20+21+23+22+24+25+27+26 = 378 = A000217(27).

%t Series[(1+2*x-x^2+2*x^3)/(1-x-x^4+x^5), {x, 0, 48}] // CoefficientList[#, x]& // Accumulate // Prepend[#, 0]& (* _Jean-François Alcover_, Apr 30 2013 *)

%o (PARI) concat([0],Vec(-x*(2*x^3-x^2+2*x+1) / ((x-1)^3*(x+1)*(x^2+1))+O(x^66))) \\ _Joerg Arndt_, Apr 30 2013

%Y Cf. A000217, A116966.

%K easy,nonn

%O 0,3

%A _Jonathan Vos Post_, Apr 02 2006

%E More terms from _Colin Barker_, Apr 30 2013