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A081441 a(n) = (2*n^3 - n^2 - n + 2)/2. 3
1, 1, 6, 22, 55, 111, 196, 316, 477, 685, 946, 1266, 1651, 2107, 2640, 3256, 3961, 4761, 5662, 6670, 7791, 9031, 10396, 11892, 13525, 15301, 17226, 19306, 21547, 23955, 26536, 29296, 32241, 35377, 38710, 42246, 45991, 49951, 54132, 58540, 63181 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Diagonal in array of n-gonal numbers A081422.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: (1 -4*x +11*x^2 -8*x^3)/(1-x)^5.

a(n) = (n + 1)*(2*n^2 - 3*n + 2)/2 = (n-1)*A005564(n+1) - n*A005564(n), where A005564(0..2) = 0, -1, 0. - Bruno Berselli, May 19 2015

E.g.f.: (2 + 5*x^2 + 2*x^3)*exp(x)/2. - G. C. Greubel, Aug 14 2019

MAPLE

a:= n-> (2*n^3-n^2-n+2)/2: seq(a(n), n=0..50); # Zerinvary Lajos, Sep 13 2006

MATHEMATICA

Table[(2n^3-n^2-n+2)/2, {n, 0, 40}] (* Harvey P. Dale, May 29 2012 *)

CoefficientList[Series[(1 - 4 x + 11 x^2 - 8 x^3) / (1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 08 2013 *)

PROG

(MAGMA) [(2*n^3-n^2-n+2)/2: n in [0..50]]; // Vincenzo Librandi, Aug 08 2013

(PARI) vector(40, n, n--; (2*n^3-n^2-n+2)/2) \\ G. C. Greubel, Aug 14 2019

(Sage) [(2*n^3-n^2-n+2)/2 for n in (0..40)] # G. C. Greubel, Aug 14 2019

(GAP) List([0..40]. n-> (2*n^3-n^2-n+2)/2); # G. C. Greubel, Aug 14 2019

CROSSREFS

Cf. A005564, A081422, A081436, A081437, A081438.

Sequence in context: A216894 A212692 A034134 * A127760 A320243 A066188

Adjacent sequences:  A081438 A081439 A081440 * A081442 A081443 A081444

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 21 2003

STATUS

approved

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Last modified September 19 02:57 EDT 2019. Contains 327186 sequences. (Running on oeis4.)