A044446 -id:A044446 - cp's OEIS frontend

A119413 a(n) = 16*n - 12.

4, 20, 36, 52, 68, 84, 100, 116, 132, 148, 164, 180, 196, 212, 228, 244, 260, 276, 292, 308, 324, 340, 356, 372, 388, 404, 420, 436, 452, 468, 484, 500, 516, 532, 548, 564, 580, 596, 612, 628, 644, 660, 676, 692, 708, 724, 740, 756, 772, 788, 804, 820, 836

Offset: 1

Jorge Coveiro, Jul 26 2006

General form: (q*n+1)*q: q=2: A016825, q=3: A017197, q=4: A119413, ... . - Vladimir Joseph Stephan Orlovsky, Feb 16 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..5000
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A044446, A085805, A016825, A017197, A119413.

Cf. A016813, A017089.

[16*n-12: n in [1..60]]; // Vincenzo Librandi, Jul 23 2011

Range[4, 1000, 16] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)

PARI
```
for(x=1,100,print1(16*x-12,", "))
```

O.g.f.: 4*x*(1+3*x)/(1-x)^2. - R. J. Mathar, Aug 08 2008
From Elmo R. Oliveira, Apr 03 2025: (Start)
E.g.f.: 4*(exp(x)*(4*x - 3) + 3).
a(n) = 2*a(n-1) - a(n-2) for n > 2.
a(n) = 4*A016813(n-1) = 2*A017089(n-1). (End)

A043880 Numbers k such that 0 and 1 occur juxtaposed in the base-4 representation of k but not of k+1.

Original entry on oeis.org

4, 20, 33, 36, 49, 52, 84, 97, 100, 113, 116, 129, 135, 148, 161, 164, 177, 180, 193, 199, 212, 225, 228, 241, 244, 340, 353, 356, 369, 372, 385, 391, 404, 417, 420, 433, 436, 449, 455, 468, 481, 484, 497, 500, 513, 519, 543, 545, 548, 561, 564, 596, 609, 612

Offset: 1

Clark Kimberling

Cf. A007090, A044446.

SequencePosition[Table[If[SequenceCount[IntegerDigits[n,4],{0,1}]>0 || SequenceCount[ IntegerDigits[ n,4],{1,0}]>0,1,0],{n,600}],{1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 14 2016 *)

from sympy.ntheory.factor_ import digits
def has01or10(k):
  s = "".join(map(str, digits(k, 4)[1:])); return "01" in s or "10" in s
def ok(n): return has01or10(n) and not has01or10(n+1)
print(list(filter(ok, range(613)))) # Michael S. Branicky, Apr 20 2021

cp's OEIS Frontend

A119413 a(n) = 16*n - 12.

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