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A034721 a(n) = (10*n^3 - 9*n^2 + 2*n)/3 + 1. 1
1, 2, 17, 66, 169, 346, 617, 1002, 1521, 2194, 3041, 4082, 5337, 6826, 8569, 10586, 12897, 15522, 18481, 21794, 25481, 29562, 34057, 38986, 44369, 50226, 56577, 63442, 70841, 78794, 87321, 96442, 106177, 116546, 127569, 139266, 151657 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = A034720(n) + 1 for n > 0, where +1 counts the empty string.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 21 2012

G.f.: (1 - 2*x + 15x^2 + 6x^3)/(1-x)^4. - Bruno Berselli, Jun 21 2012

E.g.f.: (3 + 3*x + 21*x^2 + 10*x^3)*exp(x)/3. - G. C. Greubel, Nov 11 2019

MAPLE

seq((10*n^3 -9*n^2 +2*n +3)/3, n=0..40); # G. C. Greubel, Nov 11 2019

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {1, 2, 17, 66}, 40] (* Vincenzo Librandi, Jun 21 2012 *)

PROG

(PARI) a(n)=(10*n^3-9*n^2+2*n)/3+1 \\ Charles R Greathouse IV, Dec 08 2011

(MAGMA) I:=[1, 2, 17, 66]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 21 2012

(Sage) [(10*n^3 -9*n^2 +2*n +3)/3 for n in (0..40)] # G. C. Greubel, Nov 11 2019

(GAP) List([0..40], n-> (10*n^3 -9*n^2 +2*n +3)/3); # G. C. Greubel, Nov 11 2019

CROSSREFS

Cf. A034720.

Sequence in context: A176581 A303374 A037420 * A281708 A107815 A042803

Adjacent sequences:  A034718 A034719 A034720 * A034722 A034723 A034724

KEYWORD

nonn,easy

AUTHOR

Felice Russo

EXTENSIONS

Edited by Frank Ellermann, Mar 13 2002

STATUS

approved

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Last modified December 11 18:34 EST 2019. Contains 329925 sequences. (Running on oeis4.)