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A195014
Vertex number of a square spiral whose edges have length A195013.
11
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
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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 09 2011
STATUS
approved