A157517 a(n) = 7 + 12*n - 6*n^2.

7, 13, 7, -11, -41, -83, -137, -203, -281, -371, -473, -587, -713, -851, -1001, -1163, -1337, -1523, -1721, -1931, -2153, -2387, -2633, -2891, -3161, -3443, -3737, -4043, -4361, -4691, -5033, -5387, -5753, -6131, -6521, -6923, -7337, -7763, -8201, -8651

Offset

0,1

Comments

From John Couch Adams multisteps integration of differential equations, 1855.

References

P. Curtz Integration numerique des systemes differentiels, C.C.S.A., Arcueil, 1969, p. 36.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = 12*n + 6 - A140811(n) = A017593(n) - A140811(n).

Recurrences: a(n) = 2*a(n-1) - a(n-2) - 12 = 3*a(n-1) - 3*a(n-2) + a(n-3).

First differences: a(n+1) - a(n) = -A017593(n-1), n > 0. Second differences are all -12.

a(n+2) - a(n) = -A008606(n).

G.f.: (-7 + 8*x + 11*x^2)/(x-1)^3. - R. J. Mathar, Mar 15 2009

Prog

(Magma) [7+12*n-6*n^2: n in [0..50]]; // Vincenzo Librandi, Aug 07 2011
(PARI) a(n)=7+12*n-6*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A134039 A125741 A103705 * A164929 A357127 A081257

Adjacent sequences: A157514 A157515 A157516 * A157518 A157519 A157520

Keyword

sign,easy

Author

Paul Curtz, Mar 02 2009

Extensions

Edited and extended by R. J. Mathar, Mar 15 2009

Status

approved