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A266491 a(n) = n*A130658(n). 0
0, 1, 4, 6, 4, 5, 12, 14, 8, 9, 20, 22, 12, 13, 28, 30, 16, 17, 36, 38, 20, 21, 44, 46, 24, 25, 52, 54, 28, 29, 60, 62, 32, 33, 68, 70, 36, 37, 76, 78, 40, 41, 84, 86, 44, 45, 92, 94, 48, 49, 100, 102, 52, 53, 108, 110, 56, 57, 116, 118, 60, 61, 124, 126, 64 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Successive differences:

r(0):    0,   1,    4,    6,   4,    5,   12,   14, ...

r(1):    1,   3,    2,   -2,   1,    7,    2,   -6, ...

r(2):    2,  -1,   -4,    3,   6,   -5,   -8,    7, ... (see A103889)

r(3):   -3,  -3,    7,    3, -11,   -3,   15,    3, ...

r(4):    0,  10,   -4,  -14,   8,   18,  -12,  -22, ...

r(5):   10, -14,  -10,   22,  10,  -30,  -10,   38, ...

r(6):  -24,   4,   32,  -12, -40,   20,   48,  -28, ...

r(7):   28,  28,  -44,  -28,  60,   28,  -76,  -28, ...

r(8):    0, -72,   16,   88, -32, -104,   48,  120, ...

r(9):  -72,  88,   72, -120, -72,  152,   72, -184, ...

r(10): 160, -16, -192,   48, 224,  -80, -256,  112, ...

etc.

Let b(n) = 1, 1, 1, 1, 2, 2, 4, 4, 8, 8, 16, 16, ..., with n>=0, which is formed from the terms of A011782 repeated twice.

Conjecture: all terms of the row r(i) are divisible by b(i).

Conjecture: the terms of the first column divided by b(n) provide 0, 1, 2, -3, 0, 5, -6, 7, 0, -9, 10, -11, ..., the absolute values of which are listed in A190621.

LINKS

Table of n, a(n) for n=0..64.

FORMULA

a(n) = n*(3 - (-1)^((n-1)*n/2))/2.

a(n) = a(n-4) + 4*A130658(n) for n>3.

a(n) = 2*a(n-1) -3*a(n-2) +4*a(n-3) -3*(n-4) +2*a(n-5) -a(n-6) for n>5.

G.f.: x*(3/(1 - x)^2 + 2*x/(1 + x^2)^2 - (1 - x^2)/(1 + x^2)^2)/2. - Michael De Vlieger, Jan 04 2016

MATHEMATICA

Table[n (3 - (-1)^((n - 1) n/2))/2, {n, 0, 55}]

Table[n (Boole@ OddQ@ Floor[n/2] + 1), {n, 0, 55}] (* or *) Table[SeriesCoefficient[x (3/(1 - x)^2 + 2 x/(1 + x^2)^2 - (1 - x^2)/(1 + x^2)^2)/2, {x, 0, n}], {n, 0, 55}] (* Michael De Vlieger, Jan 04 2016 *)

PROG

(PARI) vector(60, n, n--; n*(3-(-1)^((n-1)*n/2))/2) \\ Altug Alkan, Jan 04 2016

(MAGMA) [n*(3-(-1)^((n-1)*n div 2))/2: n in [0..70]]; // Vincenzo Librandi, Jan 08 2016

CROSSREFS

Cf. A005408, A011782, A042963, A058962, A103889, A128135, A130658, A190621, A227380.

Sequence in context: A243371 A123999 A014110 * A323016 A261637 A091651

Adjacent sequences:  A266488 A266489 A266490 * A266492 A266493 A266494

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Dec 30 2015

EXTENSIONS

Edited by Bruno Berselli, Jan 07 2016

STATUS

approved

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Last modified May 17 05:13 EDT 2021. Contains 343965 sequences. (Running on oeis4.)