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A283551 a(n) = -1 + 5*n/6 + n^3/6. 1
-1, 0, 2, 6, 13, 24, 40, 62, 91, 128, 174, 230, 297, 376, 468, 574, 695, 832, 986, 1158, 1349, 1560, 1792, 2046, 2323, 2624, 2950, 3302, 3681, 4088, 4524, 4990, 5487, 6016, 6578, 7174, 7805, 8472, 9176, 9918, 10699, 11520, 12382, 13286, 14233, 15224, 16260 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) - a(-n) = 2*a(n) + 2 = A033547(n).

(a(n+10) - a(n-10))/10 = 36, 35, 36, 39, 44, 51, ... .

a(n) is in the fifth line of

0,     0,  0,  0,  0,  0, 0, 0, 0,  0,  0,  0,   0,   0, ...

1,     1,  1,  1,  1,  1, 1, 1, 1,  1,  1,  1,   1,   1, ...

-6,   -5, -4, -3, -2, -1, 0, 1, 2,  3,  4,  5,   6,   7, ...

16,   11,  7,  4,  2,  1, 1, 2, 4,  7, 11, 16,  22,  29, ...

-26, -15, -8, -4, -2, -1, 0, 2, 6, 13, 24, 40,  62,  91, ...

31,   16,  8,  4,  2,  1, 1, 3, 9, 22, 46, 86, 148, 239, ...

etc.

First line: A000004. Second line: A000012. Third line: (from 0) A001477 and (backwards) -A001477. Fourth line: (from the second 1 and from the first 1) A000124(n). Fifth line: (from -1) a(n) and -A000125(n). Sixth line: (from 3) A223718, (from the first 1) A000127(n), the second 1 is a separatrix. For the sixth, eighth and tenth lines, Ron Hardin found A223718(n), A223659(n), A225011(n).

LINKS

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(-n) = - a(n) - 2 = -1, -2, -4, -8, -15, -26, -42, ... = -A000125(n).

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

a(n) = a(n-1) + A000124(n).

G.f.: (2*x^3 -4*x^2 +4*x -1)/(x -1)^4. - Robert G. Wilson v, Mar 15 2017

MAPLE

A283551:=n->-1 + 5*n/6 + n^3/6: seq(A283551(n), n=0..100); # Wesley Ivan Hurt, Oct 03 2017

MATHEMATICA

Table[-1 + 5 n/6 + n^3/6, {n, 0, 39}] (* Michael De Vlieger, Mar 15 2017 *)

CoefficientList[ Series[(2x^3 -4x^2 +4x -1)/(x -1)^4, {x, 0, 50}], x] (* or *)

LinearRecurrence[{4, -6, 4, -1}, {-1, 0, 2, 6}, 50] (* Robert G. Wilson v, Mar 15 2017 *)

PROG

(MAGMA) [-1 + 5*n/6 + n^3/6 : n in [0..60]]; // Wesley Ivan Hurt, Oct 03 2017

CROSSREFS

Essentially a duplicate of A003600.

Cf. A000124, A000125, A033547, A059259, A220074.

Sequence in context: A338991 A178532 A003600 * A000135 A281865 A267698

Adjacent sequences:  A283548 A283549 A283550 * A283552 A283553 A283554

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Mar 10 2017

EXTENSIONS

Corrected by Jeremy Gardiner, Jan 29 2019

STATUS

approved

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)