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

Author

Paul Barry, Mar 21 2003

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A081435, A081436, A081437.

Programs

GAP

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

Magma

[(2*n^3+n^2+n+2)/2: n in [0..40]]; // Vincenzo Librandi, Aug 08 2013

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 *)

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

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