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A116996 Partial sums of A116966. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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 A217836

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

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Last modified September 28 02:29 EDT 2020. Contains 337392 sequences. (Running on oeis4.)