A068073 -id:A068073 - cp's OEIS frontend

A175828 a(n) = (n(6n+1)+(n+2)*(-1)^n)/2.

1, 2, 15, 26, 53, 74, 115, 146, 201, 242, 311, 362, 445, 506, 603, 674, 785, 866, 991, 1082, 1221, 1322, 1475, 1586, 1753, 1874, 2055, 2186, 2381, 2522, 2731, 2882, 3105, 3266, 3503, 3674, 3925, 4106, 4371, 4562, 4841, 5042, 5335, 5546, 5853, 6074

Offset: 0

Bruno Berselli, Sep 21 2010 - Sep 25 2010

a(n) == A068073(n) (mod 4).

a(h) == 0 (mod 11) for h = 11*(k-floor((k-1)/3))-2*(-1)^(k+floor(k/3)) (cf. A175833).

Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Cf. A068073, A010718, A142241, A175833.

[(n*(6*n+1)+(n+2)*(-1)^n)/2: n in [0..50]];

I:=[1,2,15,26,53]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Aug 19 2013

Table[(n (6 n + 1) + (n + 2) (-1)^n)/2, {n, 0, 50}]
CoefficientList[Series[(1 + x + 11 x^2 + 9 x^3 + 2 x^4) / ((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 19 2013 *)
LinearRecurrence[{1,2,-2,-1,1},{1,2,15,26,53},70] (* Harvey P. Dale, Jul 03 2019 *)

G.f.: (1+x+11*x^2+9*x^3+2*x^4)/((1+x)^2*(1-x)^3).
a(n)-a(n-1)-2*a(n-2)+2*a(n-3)+a(n-4)-a(n-5) = 0 for n>4.
a(n)-a(n-2)-(a(n-1)-a(n-3)) = 2*A010718(n-1) for n>2.
a(n)-a(n-2)+(a(n-1)-a(n-3)) = A142241(n-2) for n>2.

A262734 Period 16: repeat (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9

Offset: 0

Ilya Gutkovskiy, Sep 29 2015

Decimal expansion of 111111112/900000009.

For n which lies in the interval [16*(k-1), 8*(2*k-1)], where k>0 -> pattern {1, 2, 3, 4, 5, 6, 7, 8, 9}; for n which lies in the interval [16*k - 7, 16*k - 1], where k>0 -> pattern {8, 7, 6, 5, 4, 3, 2}.

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,-1,1).

Cf. A158289, A177274, A010889, A138531, A181975, A199264, A068073, A028356.

&cat[[1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2]: n in [0..10]]; // Vincenzo Librandi, Sep 29 2015

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, -1, 1}, {1, 2, 3, 4, 5, 6, 7, 8, 9}, 120] (* Vincenzo Librandi, Sep 29 2015 *)

Vec(-(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1)/((x-1)*(x^8+1)) + O(x^100)) \\ Colin Barker, Sep 29 2015

111111112/900000009. \\ Altug Alkan, Sep 29 2015

vector(200, n, default(realprecision, n+2); floor(111111112/900000009*10^n)%10) \\ Altug Alkan, Nov 12 2015

-1 + a(16*(k - 1)) = -2 + a(8*k + 3*(-1)^k - 4) = -3 + a(2*(4*k + (-1)^k - 2)) = -4 + a(8*k + (-1)^k - 4) = -5 + a(4*(2*k - 1)) = -6 + a(8*k - (-1)^k - 4) = -7 + a(-2*(-4*k + (-1)^k + 2)) = -8 + a(8*k - 3*(-1)^k - 4) = -9 + a(8*(2*k - 11)) = 0, for k>0.
a(0) = 1, a(n) = a(n+1) - 1, for 16*(k - 1) <= n < 8*(2*k - 1), and a(n) = a(n + 1) + 1, for 8*(2*k - 1) <= n < 16*k, where k>0.
From Colin Barker, Sep 29 2015: (Start)
a(n) = a(n-1) - a(n-8) + a(n-9) for n>8.
G.f.: -(2*x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1) / ((x-1)*(x^8+1)). (End)

cp's OEIS Frontend

A175828 a(n) = (n(6n+1)+(n+2)*(-1)^n)/2.

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A262734 Period 16: repeat (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2).

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cp's OEIS Frontend

A175828 a(n) = (n*(6*n+1)+(n+2)*(-1)^n)/2.

Views

Author

Keywords

Comments

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Crossrefs

Programs

Magma

Magma

Mathematica

Formula

A262734 Period 16: repeat (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2).

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Author

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Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

PARI

PARI

Formula

A175828 a(n) = (n(6n+1)+(n+2)*(-1)^n)/2.