A241807 Numerators of c(n) = (n^2+n+2)/((n+1)*(n+2)*(n+3)) as defined in A241269.

1, 1, 2, 7, 11, 2, 11, 29, 37, 23, 28, 67, 79, 23, 53, 121, 137, 77, 86, 191, 211, 29, 127, 277, 301, 163, 176, 379, 407, 109, 233, 497, 529, 281, 298, 631, 667, 88, 371, 781, 821, 431, 452, 947, 991, 259, 541, 1129, 1177, 613, 638

Offset

0,3

Comments

The subsequence 1, 23, 77, 163, 281, 431, 613, 827, ..., with indices congruent to 1 mod 8, is 16n^2+6n+1, that is, A000124(8n+1)/2 or A014206(8n+1)/4. Its second differences are constant: (16n^2+6n+1)'' = 32.

The sequence A014206/A241807 is integral and consists of the 16-periodic sequence (2, 4, 4, 2, 2, 16, 4, 2, 2, 4, 4, 2, 2, 8, 4, 2, ...).

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = A014206(n)/period 16: repeat 2, 4, 4, 2, 2, 16, 4, 2, 2, 4, 4, 2, 2, 8, 4, 2 (conjectured).

a(4k) = 8*k^2 +2*k +1,

a(4k+2) = 4*k^2 +5*k +2,

a(4k+3) = 8*k^2 +14*k +7,

a(8k+1) = 16*k^2 +6*k +1,

a(16k+5) = 16*k^2 +11*k +2,

a(16k+13) = 32*k^2 + 54*k +23.

Example

1/3, 1/6, 2/15, 7/60, 11/105, 2/21, 11/126, 29/360, 37/495, 23/330, ...

Mathematica

Table[(n^2+n+2)/((n+1)*(n+2)*(n+3)) // Numerator, {n, 0, 50}]

Crossrefs

Cf. A000124, A014206, A241269, A188135, A054552, A185438.

Sequence in context: A179117 A133154 A100020 * A020638 A091385 A053247

Adjacent sequences: A241804 A241805 A241806 * A241808 A241809 A241810

Keyword

nonn,frac

Author

Jean-François Alcover and Paul Curtz, Apr 29 2014

Status

approved