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URL: https://oeis.org/A123203

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A123203
a(n) = 2^(n+1) - 3*n.
9
1, 2, 7, 20, 49, 110, 235, 488, 997, 2018, 4063, 8156, 16345, 32726, 65491, 131024, 262093, 524234, 1048519, 2097092, 4194241, 8388542, 16777147, 33554360, 67108789, 134217650, 268435375, 536870828, 1073741737, 2147483558
OFFSET
1,2
COMMENTS
An elephant sequence, see A175654. For the corner squares just one A[5] vector, with decimal value 186, leads to this sequence. For the central square this vector leads to the companion sequence A036563. - Johannes W. Meijer, Aug 15 2010
LINKS
Joseph Breen and Emma Copeland, Non-orientable Nurikabe, arXiv:2506.12612 [math.CO], 2025. See pp. 1, 4.
Tamas Lengyel, On p-adic properties of the Stirling numbers of the first kind, Journal of Number Theory, 148 (2015) 73-94.
FORMULA
Binomial transform of [1, 1, 4, 4, 4, ...].
Equals row sums of triangle A131061.
From Johannes W. Meijer, Aug 15 2010; corrected by Colin Barker, Jul 28 2012: (Start)
a(n) = 2^(1+n) - 3*n.
a(n) = 3*A000295(n-1) + A000079(n-1).
(End)
G.f.: x*(1 - 2*x + 4*x^2)/((1-x)^2*(1-2*x)). - Colin Barker, Jul 28 2012
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Colin Barker, Jul 29 2012
E.g.f.: 2*exp(2*x) - 3*x*exp(x) - 2. - G. C. Greubel, Sep 14 2024
EXAMPLE
a(4) = 20, row sums of 4th row of triangle A131062: (1, 9, 9, 1).
a(4) = 20 = (1, 3, 3, 1) dot (1, 1, 4, 4) = (1 + 3 + 12 + 4).
MATHEMATICA
Table[2^(n+1) - 3*n, {n, 40}] (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)
LinearRecurrence[{4, -5, 2}, {1, 2, 7}, 40] (* Harvey P. Dale, Mar 30 2024 *)
PROG
(Magma) [2^(n+1) -3*n: n in [1..40]]; // G. C. Greubel, Sep 14 2024
(SageMath)
def A123203(n): return 2^(n+1) -3*n
[A123203(n) for n in range(1, 41)] # G. C. Greubel, Sep 14 2024
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 13 2007
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Nov 15 2008
Title changed by G. C. Greubel, Sep 14 2024
STATUS
approved