A010019 a(0) = 1, a(n) = 29*n^2 + 2 for n>0.

1, 31, 118, 263, 466, 727, 1046, 1423, 1858, 2351, 2902, 3511, 4178, 4903, 5686, 6527, 7426, 8383, 9398, 10471, 11602, 12791, 14038, 15343, 16706, 18127, 19606, 21143, 22738, 24391, 26102, 27871, 29698, 31583, 33526, 35527, 37586, 39703, 41878, 44111, 46402

Offset

0,2

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: (1+x)*(1+27*x+x^2)/(1-x)^3. - Bruno Berselli, Feb 07 2012

E.g.f.: (x*(x+1)*29+2)*e^x-1. - Gopinath A. R., Feb 14 2012

Mathematica

Join[{1}, 29 Range[40]^2 + 2] (* Bruno Berselli, Feb 07 2012 *)
Join[{1}, LinearRecurrence[{3, -3, 1}, {31, 118, 263}, 50]] (* Vincenzo Librandi, Aug 03 2015 *)

Prog

(PARI) a(n)=polcoeff((x*(x+1)*29+2)*exp(x+O(x^(n+1)))-1, n)*n!  /* to illustrate the e.g.f. */
(PARI) A010019(n)=29*n^2+2-!n   \\ M. F. Hasler, Feb 14 2012
(Magma) [1] cat [29*n^2+2: n in [1..50]]; // Vincenzo Librandi, Aug 03 2015

Crossrefs

Cf. similar sequences listed in A206399.

Sequence in context: A304241 A204735 A254283 * A256650 A131550 A360805

Adjacent sequences: A010016 A010017 A010018 * A010020 A010021 A010022

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved