A275591 a(n) = n^2 + 9*n + 1.

1, 11, 23, 37, 53, 71, 91, 113, 137, 163, 191, 221, 253, 287, 323, 361, 401, 443, 487, 533, 581, 631, 683, 737, 793, 851, 911, 973, 1037, 1103, 1171, 1241, 1313, 1387, 1463, 1541, 1621, 1703, 1787, 1873, 1961, 2051, 2143, 2237, 2333, 2431, 2531, 2633, 2737

Offset: 0

Author

Miquel Cerda, Aug 02 2016

Keywords

• nonn
• easy

Comments

Also, nonnegative integers m such that 4*m + 77 is a square. The negative values of m are -7, -13, -17, -19.

The product of two consecutive terms belongs to the sequence. In fact: a(k)*a(k+1) = a(k*(k+1)+9*k+1).

Links

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

Crossrefs

Cf. A028569.

Subsequence of A007775.

Programs

Mathematica

Table[n^2 + 9 n + 1, {n, 0, 50}] (* Bruno Berselli, Aug 05 2016 *)

PARI

a(n) = n^2 + 9*n + 1 \\ Charles R Greathouse IV, Aug 03 2016

PARI

Vec((1+8*x-7*x^2)/(1-x)^3 + O(x^100)) \\ Colin Barker, Aug 04 2016

Formula

O.g.f.: (1 + 8*x - 7*x^2)/(1 - x)^3. - Colin Barker, Aug 03 2016

E.g.f.: (1 + 10*x + x^2)*exp(x).

a(n) = a(-n-9) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Colin Barker, Aug 03 2016

a(n) = A048058(n-1) + A008592(n-1) for n>0.

a(n) = 1 + A028569(n). - Omar E. Pol, Aug 02 2016

a(n) + a(-n) = (n-1)^2 + (n+1)^2.

Sum_{i>=0} 1/a(i) = 9736/29393 + tan(sqrt(77)*Pi/2)*Pi/sqrt(77) = 1.301517...

Extensions

Edited and extended by Bruno Berselli, Aug 05 2016