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A081423 Subdiagonal of array of n-gonal numbers A081422. 4
1, 3, 12, 34, 75, 141, 238, 372, 549, 775, 1056, 1398, 1807, 2289, 2850, 3496, 4233, 5067, 6004, 7050, 8211, 9493, 10902, 12444, 14125, 15951, 17928, 20062, 22359, 24825, 27466, 30288, 33297, 36499, 39900, 43506, 47323, 51357, 55614, 60100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

One of a family of sequences with palindromic generators.

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) = (2*n^3 + n^2 + n + 2)/2.

G.f.: (1 -2*x +7*x^2 -6*x^3)/(1-x)^5.

E.g.f.: (2 +4*x +7*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..40); # G. C. Greubel, Aug 14 2019

MATHEMATICA

CoefficientList[Series[(1 -2x +7x^2 -6x^3)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 08 2013 *)

PROG

(MAGMA) [(2*n^3+n^2+n+2)/2: n in [0..40]]; // 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. A081435, A081436, A081437.

Sequence in context: A183468 A196234 A117655 * A184705 A257890 A060298

Adjacent sequences:  A081420 A081421 A081422 * A081424 A081425 A081426

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 21 2003

STATUS

approved

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Last modified July 25 15:30 EDT 2021. Contains 346291 sequences. (Running on oeis4.)