A083817 Interleaving of (1,2,3,4,5,...), (2,2,2,2,...) and (0,1,3,6,10,...).

1, 2, 0, 2, 2, 1, 3, 2, 3, 4, 2, 6, 5, 2, 10, 6, 2, 15, 7, 2, 21, 8, 2, 28, 9, 2, 36, 10, 2, 45, 11, 2, 55, 12, 2, 66, 13, 2, 78, 14, 2, 91, 15, 2, 105, 16, 2, 120, 17, 2, 136, 18, 2, 153, 19, 2, 171, 20, 2, 190, 21, 2, 210, 22, 2, 231, 23, 2, 253, 24, 2, 276, 25, 2, 300, 26, 2

Offset

0,2

Links

Table of n, a(n) for n=0..76.

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Formula

G.f.: -(2*x^7+x^5-4*x^4-x^3+2*x+1) / ((x-1)^3*(x^2+x+1)^3). - Colin Barker, Jul 31 2013

Maple

a := proc(n) if n mod 3 = 0 then RETURN(n/3+1) fi: if n mod 3 = 1 then RETURN(2) fi: if n mod 3 = 2 then RETURN(((n-2)/3)*((n-2)/3+1)/2) fi: end: for n from 0 to 150 do printf(`%d, `, a(n)) od:

Mathematica

Flatten[ Table[ {n, 2, n(n - 1)/2}, {n, 1, 27}]]
With[{nn=30}, Riffle[Riffle[Range[nn], Accumulate[Range[0, nn]], {2, -1, 2}], 2, {2, -1, 3}]] (* Harvey P. Dale, May 20 2013 *)

Crossrefs

Sequence in context: A128664 A003823 A059451 * A286222 A029273 A117963

Adjacent sequences: A083814 A083815 A083816 * A083818 A083819 A083820

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 18 2003

Extensions

More terms from James A. Sellers and Robert G. Wilson v, Jun 21 2003

Status

approved