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A163761 a(n) = 10*n*(n+1). 2
0, 20, 60, 120, 200, 300, 420, 560, 720, 900, 1100, 1320, 1560, 1820, 2100, 2400, 2720, 3060, 3420, 3800, 4200, 4620, 5060, 5520, 6000, 6500, 7020, 7560, 8120, 8700, 9300, 9920, 10560, 11220, 11900, 12600, 13320, 14060, 14820, 15600, 16400, 17220, 18060 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

20 times the n-th triangular number.

a(n) is the number of one-sided n-step prudent walks, from (0,0) to (3,3), for n-6 is even. - Shanzhen Gao, Apr 26 2011

Numbers k such that 10*k + 25 is a square. -  Bruno Berselli, May 14 2018

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..875

John Elias, Illustration of Initial Terms: Correlation of 10k+25 is a square

Shanzhen Gao and Keh-Hsun Chen, Tackling Sequences From Prudent Self-Avoiding Walks, FCS'14, The 2014 International Conference on Foundations of Computer Science.

Shanzhen Gao and H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, (submitted to INTEGERS: The Electronic Journal of Combinatorial Number Theory).

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

FORMULA

a(n) = 20*A000217(n) = 10*A002378(n).

G.f.: 20*x/(1-x)^3.

E.g.f.: 10*x*(x+2)*exp(x). - G. C. Greubel, Aug 03 2017

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {0, 20, 60}, 50] (* or *) Table[10*n*(n+1), {n, 0, 50}] (* G. C. Greubel, Aug 03 2017 *)

PROG

(Magma) [10*n*(n+1): n in [0..50]];

(PARI) a(n)=10*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A000217, A002378.

Sequence in context: A220046 A275167 A344200 * A154072 A078184 A116530

Adjacent sequences:  A163758 A163759 A163760 * A163762 A163763 A163764

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Aug 03 2009

EXTENSIONS

Entries checked by R. J. Mathar, Aug 06 2009

STATUS

approved

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Last modified September 27 03:24 EDT 2022. Contains 357051 sequences. (Running on oeis4.)