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A121991

a(n) = 3*a(n-1) - a(n-2) - a(n-3) + 12.

0, 1, 13, 50, 148, 393, 993, 2450, 5976, 14497, 35077, 84770, 204748, 494409, 1193721, 2882018, 6957936, 16798081, 40554301, 97906898, 236368324, 570643785, 1377656145, 3325956338, 8029569096, 19385094817

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OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4, -4, 0, 1).

FORMULA

a(n) = ((11 - 7*sqrt(2))*(1 - sqrt(2))^n + (1 + sqrt(2))^n*(11 + 7*sqrt(2)) - 24*n - 22)/4.

O.g.f.: -x(1+9x+2x^2)/((1-x)^2*(x^2+2x-1)). - R. J. Mathar, Aug 22 2008

a(n) = -6(n+1)+(1+11*A000129(n+1)+3*A000129(n))/2. - R. J. Mathar, Aug 22 2008

E.g.f.: (1/2)*(11*cosh(sqrt(2)*x) + 7*sqrt(2)*sinh(sqrt(2)*x) - (12*x + 11))*exp(x). - G. C. Greubel, Sep 14 2017

a(n) = 4*a(n-1) - 4*a(n-2) + a(n-4). - Wesley Ivan Hurt, May 04 2024

MATHEMATICA

RecurrenceTable[{a[n] == 3*a[n - 1] - a[n - 2] - a[n - 3] + 12, a[0] == 0, a[1] == 1, a[2] == 13}, a, {n, 0, 50}] (* or *) LinearRecurrence[{4, -4, 0, 1}, {0, 1, 13, 50}, 50] (* G. C. Greubel, Sep 14 2017 *)

PROG

(PARI) x='x+O('x^50); concat([0], Vec(-x*(1+9*x+2*x^2)/((1-x)^2*(x^2+2*x-1))) ) \\ G. C. Greubel, Sep 14 2017

CROSSREFS

Cf. A000129, A003215, A005891.

Sequence in context: A322615 A209995 A050410 * A121990 A050491 A392810

Adjacent sequences: A121988 A121989 A121990 * A121992 A121993 A121994

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Sep 10 2006

EXTENSIONS

Edited by N. J. A. Sloane, Aug 24 2008, Dec 30 2008

STATUS

approved

URL: https://oeis.org/A121991

⇱ A121991 - OEIS