A143101 Partial sums of A143097.

1, 3, 7, 10, 15, 22, 28, 36, 46, 55, 66, 79, 91, 105, 121, 136, 153, 172, 190, 210, 232, 253, 276, 301, 325, 351, 379, 406, 435, 466, 496, 528, 562, 595, 630, 667, 703, 741, 781, 820, 861, 904, 946, 990, 1036, 1081, 1128, 1177, 1225, 1275, 1327, 1378, 1431

Offset

1,2

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Formula

G.f.: x(1+x+2x^2-2x^3+x^4)/((1-x)^3(1+x+x^2)). [R. J. Mathar, Sep 06 2008]

a(n) = n*(n+1)/2 + (3|n) = A000217(n) + A079978(n). - Luc Rousseau, Jun 18 2017

Example

a(3) = 7 = T(3) + 1 since 3 == 0 mod 3 and T(3) = 6.
a(4) = 10 = T(4) since 4 == 1 mod 3.

Maple

A143097 := proc(n) if(n<=1)then return n: elif(n mod 3 <= 1)then return n+1-2*(n mod 3): else return n: fi: end: A143101 := proc(n) option remember: if(n=0)then return 0:else return procname(n-1)+A143097(n):fi: end:seq(A143101(n), n=1..60); # Nathaniel Johnston, Apr 30 2011

Mathematica

With[{nn=70}, Accumulate[Join[{1}, Riffle[Rest[Select[Range[nn], !Divisible[ #, 3]&]], Range[3, nn, 3], 3]]]] (* Harvey P. Dale, May 06 2012 *)

Prog

(PARI) a(n)=n*(n+1)/2+if(n%3==0, 1, 0) \\ Luc Rousseau, Jun 18 2017

Crossrefs

Cf. A000217, A143097.

Sequence in context: A085145 A320441 A353654 * A307612 A330160 A281642

Adjacent sequences: A143098 A143099 A143100 * A143102 A143103 A143104

Keyword

nonn,easy

Author

Gary W. Adamson, Jul 24 2008

Extensions

a(18) corrected by Nathaniel Johnston, Apr 30 2011

Status

approved