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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
OFFSET
0,2
COMMENTS
One of a family of sequences with palindromic generators.
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
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 21 2003
STATUS
approved