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A275591 a(n) = n^2 + 9*n + 1. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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
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...
MATHEMATICA
Table[n^2 + 9 n + 1, {n, 0, 50}] (* Bruno Berselli, Aug 05 2016 *)
PROG
(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
CROSSREFS
Cf. A028569.
Subsequence of A007775.
Sequence in context: A135978 A280915 A139493 * A250665 A339080 A077345
KEYWORD
nonn,easy
AUTHOR
Miquel Cerda, Aug 02 2016
EXTENSIONS
Edited and extended by Bruno Berselli, Aug 05 2016
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)