A261521 a(n) = n^2 + 2*n + 29.

29, 32, 37, 44, 53, 64, 77, 92, 109, 128, 149, 172, 197, 224, 253, 284, 317, 352, 389, 428, 469, 512, 557, 604, 653, 704, 757, 812, 869, 928, 989, 1052, 1117, 1184, 1253, 1324, 1397, 1472, 1549, 1628, 1709, 1792, 1877, 1964, 2053, 2144, 2237, 2332, 2429, 2528

Offset

0,1

Comments

A139851, which lists primes of the form 4x^2 + 4xy + 29y^2, contains all prime values of a(n). - Altug Alkan, Oct 02 2015

Links

Table of n, a(n) for n=0..49.

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

Formula

a(n) = a(n-1) + A005408(n), a(0) = 29, for n > 0. - Altug Alkan, Oct 02 2015

G.f.: (29 - 55*x + 28*x^2)/(1-x)^3. - Vincenzo Librandi, Oct 03 2015

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Oct 03 2015

a(n) = A005563(n) + 29. - Omar E. Pol, Oct 17 2015

Example

For n = 3, a(3) = 3^2 + 2*3 + 29 = 44.

Mathematica

Table[n^2 + 2 n + 29, {n, 0, 50}] (* Bruno Berselli, Oct 25 2015 *)
LinearRecurrence[{3, -3, 1}, {29, 32, 37}, 50] (* Harvey P. Dale, Oct 14 2023 *)

Prog

(Python) def a(x):return x*x+2*x+27
(PARI) vector(50, n, n--; n^2+2*n+29) \\ Altug Alkan, Oct 02 2015
(PARI) Vec((29 - 55*x + 28*x^2)/(1-x)^3 + O(x^100)) \\ Altug Alkan, Oct 17 2015
(Magma) [n^2+2*n+29: n in [0..50]]; // Vincenzo Librandi, Oct 03 2015

Crossrefs

Cf. A005563, A139851.

Sequence in context: A178425 A344796 A294737 * A114180 A260729 A295153

Adjacent sequences: A261518 A261519 A261520 * A261522 A261523 A261524

Keyword

nonn,easy

Author

Jake Saville, Oct 02 2015

Status

approved