A101882 Write three numbers, skip one, write three, skip two, write three, skip three... and so on.

1, 2, 3, 5, 6, 7, 10, 11, 12, 16, 17, 18, 23, 24, 25, 31, 32, 33, 40, 41, 42, 50, 51, 52, 61, 62, 63, 73, 74, 75, 86, 87, 88, 100, 101, 102, 115, 116, 117, 131, 132, 133, 148, 149, 150, 166, 167, 168, 185, 186, 187, 205, 206, 207, 226, 227, 228, 248, 249, 250, 271

Offset: 1

Author

Candace Mills (scorpiocand(AT)yahoo.com), Dec 19 2004

Keywords

• easy
• nonn

Comments

Union of A052905, A052905+1, and A052905+2. - Ivan Neretin, Aug 03 2016

First terms of the 3 repeated terms belong to A052905. - Michael De Vlieger, Aug 03 2016

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

Crossrefs

Cf. A000217, A052905, A101881, A101883.

Programs

Mathematica

Flatten@Table[(n^2 + 5 n - 4)/2 + {0, 1, 2}, {n, 20}] (* Ivan Neretin, Aug 03 2016 *)
Table[Range[#, # + 2] &[(n^2 + 7 n + 2)/2], {n, 0, 20}] // Flatten (* or *)
Rest@ CoefficientList[Series[x (1 + x + x^2 - x^4 - x^5)/((1 + x + x^2)^2 (1 - x)^3), {x, 0, 61}], x] (* Michael De Vlieger, Aug 03 2016 *)
LinearRecurrence[{1,0,2,-2,0,-1,1},{1,2,3,5,6,7,10},70] (* Harvey P. Dale, Dec 26 2019 *)

PARI

a(n)=my(k=n%3); if(k==2, n^2+17*n-2, k==1, n^2+19*n-2, n^2+15*n)/18 \\ Charles R Greathouse IV, Aug 03 2016

Formula

G.f.: x*(1+x+x^2-x^4-x^5)/ ((1+x+x^2)^2 * (1-x)^3). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; checked and corrected by R. J. Mathar, Sep 16 2009]

a(n) = n + k * (k+1) / 2 where k = floor((n-1) / 3). - Ziad Ahmed, Jun 17 2025