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A241807 Numerators of c(n) = (n^2+n+2)/((n+1)*(n+2)*(n+3)) as defined in A241269. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover and Paul Curtz, Apr 29 2014

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)