A257352 Expansion of 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, 35151, 37051, 39001, 41001

Offset

0,3

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).

Formula

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

From Elmo R. Oliveira, Dec 10 2025: (Start)

E.g.f.: exp(x)*(1 + 25*x^2).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

a(n) = 50 * A161680(n) + 1. - Alois P. Heinz, Dec 10 2025

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 *)

Prog

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

Crossrefs

Cf. A028387, A161680, A257574.

Sequence in context: A348000 A044383 A044764 * A353599 A008883 A327624

Adjacent sequences: A257349 A257350 A257351 * A257353 A257354 A257355

Keyword

nonn,easy

Author

N. J. A. Sloane, May 03 2015

Status

approved