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

Author

Gary W. Adamson, Jul 24 2008

Keywords

• nonn
• easy

Examples

			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.
		

Links

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

Crossrefs

Cf. A000217, A143097.

Programs

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 *)

PARI

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

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

Extensions

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