A116996 Partial sums of A116966.

0, 1, 4, 6, 10, 15, 22, 28, 36, 45, 56, 66, 78, 91, 106, 120, 136, 153, 172, 190, 210, 231, 254, 276, 300, 325, 352, 378, 406, 435, 466, 496, 528, 561, 596, 630, 666, 703, 742, 780, 820, 861, 904, 946, 990, 1035, 1082, 1128, 1176, 1225

Offset: 0

Author

Jonathan Vos Post, Apr 02 2006

Keywords

• easy
• nonn

Examples

			a(1) = 1 = A000217(1).
a(2) = 1+3 = 4 = A000217(2)+1.
a(3) = 1+3+2 = 6 = A000217(3).
a(4) = 1+3+2+4 = 10 = A000217(4).
a(5) = 1+3+2+4+5 = 15 = A000217(5).
a(6) = 1+3+2+4+5+7 = 22 = A000217(6)+1.
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).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Crossrefs

Cf. A000217, A116966.

Programs

Mathematica

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 *)

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

Formula

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.

G.f.: -x*(2*x^3-x^2+2*x+1) / ((x-1)^3*(x+1)*(x^2+1)). - Colin Barker, Apr 30 2013

Extensions

More terms from Colin Barker, Apr 30 2013