A195014 Vertex number of a square spiral whose edges have length A195013.

0, 2, 5, 9, 15, 21, 30, 38, 50, 60, 75, 87, 105, 119, 140, 156, 180, 198, 225, 245, 275, 297, 330, 354, 390, 416, 455, 483, 525, 555, 600, 632, 680, 714, 765, 801, 855, 893, 950, 990, 1050, 1092, 1155, 1199, 1265, 1311, 1380, 1428, 1500, 1550, 1625, 1677

Offset

0,2

Comments

Zero together with the partial partial sums of A195013.

Second bisection is 2, 9, 21, 38, 60, 87, 119, ...: A005476. - Omar E. Pol, Sep 25 2011

Number of pairs (x,y) with even x in {0,...,n}, odd y in {0,...,3n}, and x<y. - Clark Kimberling, Jul 02 2012

Links

Table of n, a(n) for n=0..51.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).

G.f.: f(x)/g(x), where f(x) = 2*x + 3*x^2 and g(x) = (1+x)^2 * (1-x)^3. - Clark Kimberling, Jul 02 2012

a(n) = (10*n^2 + 18*n + 3 + (2*n - 3)*(-1)^n)/16. - Luce ETIENNE, Aug 11 2014

Mathematica

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 2, 5, 9, 15}, 60] (* Harvey P. Dale, May 20 2019 *)

Prog

(Magma) [(10*n^2 + 18*n + 3 + (2*n - 3)*(-1)^n)/16 : n in [0..50]]; // Vincenzo Librandi, Oct 26 2014

Crossrefs

Cf. A005476, A028895, A195013, A195020.

Sequence in context: A101201 A184535 A033096 * A152738 A022941 A320259

Adjacent sequences: A195011 A195012 A195013 * A195015 A195016 A195017

Keyword

nonn,easy

Author

Omar E. Pol, Sep 09 2011

Status

approved