A081423 Subdiagonal of array of n-gonal numbers A081422.

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

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