A257352 G.f.: (1-2*x+51*x^2)/(1-x)^3.

1, 1, 51, 151, 301, 501, 751, 1051, 1401, 1801, 2251, 2751, 3301, 3901, 4551, 5251, 6001, 6801, 7651, 8551, 9501, 10501, 11551, 12651, 13801, 15001, 16251, 17551, 18901, 20301, 21751, 23251, 24801, 26401, 28051, 29751, 31501, 33301

Offset: 0

Author

N. J. A. Sloane, May 03 2015

Keywords

• nonn
• easy
• changed

Comments

An example of a quadratic sequence for which the continued square root map (see A257574) produces the number 2. There are infinitely many sequences with this property - another example is A028387.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Popular Computing (Calabasas, CA), The CSR Function, Vol. 4 (No. 34, Jan 1976), pages PC34-10 to PC34-11. Annotated and scanned copy.
• Herman P. Robinson, The CSR Function, Popular Computing (Calabasas, CA), Vol. 4 (No. 35, Feb 1976), pages PC35-3 to PC35-4. Annotated and scanned copy.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A257574. A028387.

Programs

Mathematica

CoefficientList[Series[(1-2x+51x^2)/(1-x)^3,{x,0,40}],x] (* or  *) LinearRecurrence[{3,-3,1},{1,1,51},40] (* Harvey P. Dale, Sep 01 2025 *)

PARI

a(n)=25*n^2-25*n+1 \\ Charles R Greathouse IV, Jun 17 2017