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

0,3

Links

Table of n, a(n) for n=0..49.

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

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

Example

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).

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 *)

Prog

(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

Crossrefs

Cf. A000217, A116966.

Sequence in context: A310586 A121214 A219047 * A004399 A247558 A373630

Adjacent sequences: A116993 A116994 A116995 * A116997 A116998 A116999

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 02 2006

Extensions

More terms from Colin Barker, Apr 30 2013

Status

approved