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A195016
a(n) = (n*(5*n+7)-(-1)^n+1)/2.
3
0, 7, 17, 34, 54, 81, 111, 148, 188, 235, 285, 342, 402, 469, 539, 616, 696, 783, 873, 970, 1070, 1177, 1287, 1404, 1524, 1651, 1781, 1918, 2058, 2205, 2355, 2512, 2672, 2839, 3009, 3186, 3366, 3553, 3743, 3940, 4140, 4347, 4557, 4774, 4994
OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 7,..., and the same line from 0, in the direction 0, 17,..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. Axis perpendicular to the main axis A195015 in the same spiral.
Also sequence found by reading the line from 0, in the direction 0, 7,..., and the same line from 0, in the direction 0, 17,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. This line is parallel to A153126 in the same spiral.
FORMULA
n*(10*n-3), if n >= 1, and (2*n+1)*(5*n+1)-1, if n >= 0, interleaved.
G.f.: x*(7+3*x)/((1+x)*(1-x)^3). - Bruno Berselli, Oct 14 2011
MATHEMATICA
LinearRecurrence[{2, 0, -2, 1}, {0, 7, 17, 34}, 50] (* Paolo Xausa, Feb 09 2024 *)
PROG
(Magma) &cat[[n*t, (n+1)*t] where t is 10*n+7: n in [0..22]]; // Bruno Berselli, Oct 14 2011
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 26 2011
EXTENSIONS
Concise definition by Bruno Berselli, Oct 14 2011
STATUS
approved