A068628 Numbers occurring twice in A068627.

0, 60, 216, 468, 816, 1260, 1800, 2436, 3168, 3996, 4920, 5940, 7056, 8268, 9576, 10980, 12480, 14076, 15768, 17556, 19440, 21420, 23496, 25668, 27936, 30300, 32760, 35316, 37968, 40716, 43560, 46500, 49536, 52668, 55896, 59220, 62640, 66156, 69768, 73476

Offset

1,2

Comments

Recall that A068627 is defined as follows: a(0) = 0, a(n) = a(n-1) + n if n does not divide a(n-1), a(n) = a(n-1) - n if n divides a(n-1), a(n) = n if a(n-1) = 0.

A068627 begins: 0,1,3,0,4,9,15,22,30,39,49,60,48,61,75,60,....

Numbers occurring twice in A068627, like 0, 60 etc. are called nodes.

Links

Table of n, a(n) for n=1..40.

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

Formula

From Elmo R. Oliveira, Jun 01 2026: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: 12*x^2*(5 + 3*x)/(1 - x)^3.

E.g.f.: 12*(exp(x)*(4*x^2 - 3*x + 3) - 3).

a(n) = 12*(4*n-3)*(n-1) = 12*A007742(n-1) = 6*A033585(n-1) = 4*A063436(n-1). (End)

Prog

(PARI) already(val, v, nb)=for (i = 1, nb, if (val == v[i], return (1)); ); return (0);
lista(nn) = {preca = 0; vm = vector(nn); for (n=1, nn, vm[n] = preca; if (preca == 0, nexta = n, if (preca % n, nexta = preca + n, nexta = preca - n); ); if (already(preca, vm, n-1), print1(preca, ", ")); preca = nexta; ); } \\ Michel Marcus, Jan 23 2014

Crossrefs

Cf. A007742, A033585, A063436, A068627.

Sequence in context: A082529 A126248 A224335 * A256985 A075287 A277990

Adjacent sequences: A068625 A068626 A068627 * A068629 A068630 A068631

Keyword

easy,nonn

Author

Amarnath Murthy, Feb 26 2002

Extensions

Name and comments edited by Michel Marcus, Jan 23 2014

Offset changed to 1 and more terms from Michel Marcus, Jan 23 2014

Status

approved